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Cited by 232Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum optics and atomic interactions

The DOI matches its Crossref record; 254 of the 257 references it cites were found in a registry or an index; 30 of the 187 sources its claims cite were checked for support.

Two-photon interference: the Hong–Ou–Mandel effect

Open access
Bouchard, Frédéric, Sit, Alicia, Zhang, Yingwen, Fickler, Robert, Miatto, Filippo M, Yao, Yuan, Sciarrino, Fabio, Karimi, Ebrahim·2021·Reports on Progress in Physics
DOI 10.1088/1361-6633/abcd7a
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Abstract

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

This review covers the Hong–Ou–Mandel (HOM) effect, or two-photon/two-particle interference, over roughly three decades since its observation. It surveys the underlying beam-splitter theory and applications in precision measurement, quantum state analysis and engineering, communication, computation, multipartite interference, and non-photonic systems.

Key findings

  • The HOM effect produces destructive interference of two-photon states exiting opposite output ports of a 50:50 beam splitter, giving the hallmark coincidence dip; for indistinguishable photons the output is \((|2_c\rangle - |2_d\rangle)/\sqrt{2}\).
  • Precision applications include HOM timing measurements with reported average accuracy of 6 attoseconds and average precision of 16 attoseconds, and quantum optical coherence tomography with an improvement in resolution by a factor of 5 compared to OCT and detection of 1 µm features.
  • Linear-optics Bell-state discrimination is limited to 50% success with one beam splitter and two detectors, but can be raised to 75% with ancillary entanglement and generally to \(1 - 2^{-N}\) with \(N\) interferences; KLM-type CZ and CNOT gates have success probabilities of 2/27 and 1/16, respectively.
  • Non-photonic HOM interference has been observed with plasmons (initial visibility \(0.43 \pm 0.02\), later up to 0.95), phonons (\(0.52 \pm 0.03\)), collective atomic excitations (\(0.89 \pm 0.06\)), atoms (Rb bunching exceeding distinguishable-atom probability by 6 standard deviations; He visibility \(0.65 \pm 0.07\)), and electrons via anti-bunching/Pauli dips.

Methods

  • Design: narrative review article, not a primary experimental study; it aggregates “the most prevalent uses of two-photon interference over the past three decades” into a coherent text.
  • Data/sample: cited theoretical and experimental literature on HOM interference, including photonic, plasmonic, phononic, atomic, and electronic systems.
  • Main analysis: thematic synthesis beginning with beam-splitter and two-photon interference theory, then covering precision measurements, quantum state analysis, quantum communication, quantum state engineering, quantum computation, multipartite/multimode generalizations, and non-photonic implementations.

Limitations

  • The paper does not state a formal limitations section.
  • Text-evident limitation: as a broad review, it does not provide a systematic search or selection protocol for the literature covered.
  • Text-evident limitations in cited experiments include the initial plasmonic HOM dip visibility being below the classical limit, phonon results having statistical significance too small to exclude classical explanations with certainty, and QOCT facing challenges such as low signal and signal artifacts.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1088/1361-6633/abcd7a

Cites

254 of 254 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

30 of 187 cited sources checked · 1 supported · 4 flagged · accuracy not yet measured

  • Premisecitation

    A two-phonon interference effect has been observed involving two trapped ions.

    “Recently, such a two-phonon interference effect has been observed involving two trapped ions [181].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [181] Poem, 2012, Two-photon path-entangled states in multimode waveguides, Phys. Rev. Lett. source

      The Abstract (page unavailable) describes an experiment on two-photon interference in multimode optical waveguides, not two-phonon interference involving trapped ions. The experimental-system passage describes laser light and photon-pair generation, rather than an ion-trap experiment. (LLM, conf=0.90)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
  • Premisecitation

    For the same bandwidth, QOCT benefits from an extra factor of 2 in resolution compared to classical OCT.

    “Moreover, for the same bandwidth, QOCT benefits from an extra factor of 2 in resolution compared to classical OCT.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [24] Dowling, 2008, Quantum optical metrology—the lowdown on high-N00N states, Contemp. Phys. source

      Section 6, “Quantum Imaging and Sensing” (page not provided), reports a factor-of-two improvement in resolving power for quantum coherence tomography. It does not specify that the comparison with classical OCT is at the same bandwidth, so that qualifier is not established by our copy. (LLM, conf=0.83)

      Experimental — accuracy not yet measured
  • Findingcitation

    A 3-dimensional QOCT image of onion-skin tissue coated with gold nanoparticles indicates a resolution of 1 μm.

    “An example of a 3-dimensional image taken via QOCT for the skin of an onion coated in gold is shown in Fig. 3; this result indicates a resolution of 1 µm.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [33] Raymer, 2010, Interference of two photons of different color, Opt. Commun. source

      The paper’s Conclusions discuss interference between photons of different colors and frequency conversion, not QOCT imaging. Searches for QOCT, onion skin, gold nanoparticles, and a 1 µm imaging resolution found no passage addressing the claimed image or resolution. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
  • Premisecitation

    The correlation noise properties at the outputs were found to be below the random partition noise (classically expected noise).

    “the correlation noise properties at the outputs were studied and found to be below the random partition noise, i.e. classically expected noise (see Fig. 10a).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [199] Crespi, 2013, Integrated multimode interferometers with arbitrary designs for photonic boson sampling, Nat. Photon. source

      The Experimental boson sampling section (pp. 3–4) reports output probability distributions for one-, two-, and three-photon experiments, but does not compare output correlation noise with random partition noise. Searches for those terms and for classical or distinguishable-particle noise comparisons found no passage establishing the claimed result. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
  • Premisecitation

    Actual plasmonic bunching was experimentally observed in 2013.

    “actual plasmonic bunching was experimentally observed in 2013 [180].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [180] Lahini, 2012, Quantum walk of two interacting bosons, Phys. Rev. A source

      The Figure 4 passage reports experimentally measured spatial bunching in thermal light, and the Abstract describes experiments in nonlinear photonic lattices. Neither passage identifies the effect as plasmonic or reports an observation in 2013, so those parts of the claim are unsupported. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • It may state two separate claims as one. 59
  • Probably not a substantial claim. 54

  • It may state two separate claims as one.

    Premisecitation

    Different plasmonic experiments achieved visibilities far beyond the classical limit up to 0.95, fully certifying the quantumness of two-plasmon interferences.

    “different experiments using different plasmonic configurations, and off-chip photon detection schemes achieved visibilities far beyond the classical limit up to 0.95 [183][184][185][186], thus fully certifying the quantumness of the two plasmon interferences.”
    Quote in the paperSubstantial claim3 of 4 sources checked
    • cites [183] Politi, 2009, Integrated quantum photonics, IEEE J. Select. Top. Quantum Electron. source
    • cites [184] Peruzzo, 2010, Quantum walks of correlated photons, Science source

      The 'Quantum walks of correlated particles' section (pp. 2, 5) describes off-chip photon detection and two-photon correlations that violate a classical limit by up to 76 standard deviations. It studies photons in a waveguide chip, not plasmons in plasmonic configurations, and does not report interference visibility of 0.95. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites [185] Poulios, 2014, Quantum walks of correlated photon pairs in two-dimensional waveguide arrays, Phys. Rev. Lett. source

      The Fig. 4 passage (indexed under Abstract; page unavailable) reports 96.8 ± 2.5% visibility, and the discussion of Fig. 3 reports violations of a classical limit. But this is an experiment with photon pairs in fused-silica waveguides, not two-plasmon interference in plasmonic configurations; it also does not report a maximum visibility of 0.95. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites [186] Owens, 2011, Two-photon quantum walks in an elliptical direct-write waveguide array, New J. Phys. source

      Section 4, “Two-photon walks” (page not provided), reports photon interference visibility of 38 ± 2%, not 0.95, in a waveguide array rather than a plasmonic configuration. Section 5, “Discussion” (page not provided), explicitly says the resulting probability distributions did not exhibit a conclusively quantum signature, contrary to the claim of full certification. (LLM, conf=0.90)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Premisecitation

    Although tritters have been used to demonstrate quantum features in the two-photon regime, only recently have three photon HOM coalescences been observed.

    “Although tritters have been used to demonstrate quantum features in the two-photon regime [138,142,143], only recently have three photon HOM coalescences been observed [141,144].”
    Quote in the paperNot a substantial claim4 of 5 sources checked
    • cites [138] Zhang, 2016, Engineering two-photon high-dimensional states through quantum interference, Sci. Adv. source

      The Introduction and Results report two-photon HOM interference and quantum-state measurements, supporting the two-photon aspect of the cited clause. But Materials and Methods identify the device as a 50:50 beamsplitter, not a tritter; this paper therefore does not support the claim that tritters were used. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
    • cites [142] Nagali, 2010, Experimental optimal cloning of four-dimensional quantum states of photons, Phys. Rev. Lett. source

      The experimental-layout passage reports HOM interference between two photons at a balanced beam splitter, and the Fig. 2 and Fig. 3 captions likewise identify two-photon coalescence. Searches for tritters and three-photon HOM coalescence found no passage in our copy addressing either attributed claim; the paper's two-photon result does not establish a tritter experiment. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [143] Bouchard, 2017, High-dimensional quantum cloning and applications to quantum hacking, Sci. Adv. source

      The citation is attached to the claim about observed three-photon HOM coalescence. The Results (Fig. 1) describe HOM coalescence curves for two photons, and Materials and Methods specifies a two-photon interference experiment at a 50:50 beam splitter; this paper reports a two-photon observation, not a three-photon one. (LLM, conf=0.88)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
    • cites [141] Navez, 2003, Cloning a real d-dimensional quantum state on the edge of the no-signaling condition, Phys. Rev. A source

      The Introduction and Discussion and Conclusion discuss quantum cloning and no-signaling, not tritters or photon interference. Searches for tritters, two-photon experiments, and three-photon Hong–Ou–Mandel coalescence found no passage addressing the claim. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
    • cites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    Bell-ports have been experimentally realized with fused optical fibers and more recently with passive and active integrated waveguide circuits.

    “They have also been experimentally realized with fused optical fibers [138] and more recently with passive [141] and active integrated waveguide circuits [142].”
    Quote in the paperNot a substantial claim3 of 3 sources checked
    • cites [138] Zhang, 2016, Engineering two-photon high-dimensional states through quantum interference, Sci. Adv. source

      The citation [142] is attached to the claim about active integrated waveguide circuits. Materials and Methods (page unavailable) describes this paper’s experimental apparatus as a beamsplitter-and-mirrors filter with Dove prisms and spatial light modulators, rather than an integrated waveguide circuit. The paper therefore does not describe the realization attributed to it. (LLM, conf=0.84)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
    • cites [141] Navez, 2003, Cloning a real d-dimensional quantum state on the edge of the no-signaling condition, Phys. Rev. A source

      The Introduction and Discussion and Conclusion address quantum cloning fidelity and no-signaling, not experimental Bell-port implementations. Searches for Bell-ports, fused optical fibers, and integrated waveguide circuits found no relevant passage in our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [142] Nagali, 2010, Experimental optimal cloning of four-dimensional quantum states of photons, Phys. Rev. Lett. source

      The experimental-layout section describes single-mode fibers used to deliver and detect photons, and beam splitters used in a ququart-cloning experiment. It does not describe Bell-ports realized with fused optical fibers. Searches for “Bell-ports” and “fused optical fibers” found no passage addressing the realization attributed to this source; the waveguide-circuit claims carry separate citations. (LLM, conf=0.74)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Premisecitation

    Higher Bell state discrimination success rates can be achieved with nonlinear optics, entanglement in auxiliary modes, or feed-forward techniques.

    “Higher success rates can be achieved with nonlinear optics [73], entanglement in auxiliary modes [74,75], or feed-forward techniques [76].”
    Quote in the paperNot a substantial claim3 of 4 sources checked
    • cites [73] Nagata, 2007, Beating the standard quantum limit with four-entangled photons, Science source

      The paper’s discussion of the four-photon interferometer and its results (main text, Fig. 3; page not provided) concerns phase sensitivity, not Bell-state discrimination. Its discussion of distinguishing two four-photon input states (main text, Fig. 2, and Additional information; pages not provided) does not address whether auxiliary-mode entanglement improves Bell-state discrimination success rates. Searches for Bell-state discrimination, auxiliary modes, nonlinear optics, and feed-forward found no passage supporting the attributed point. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [74] Afek, 2010, High-N00N states by mixing quantum and classical light, Science source
    • cites [75] Zhou, 2017, Superresolving phase measurement with short-wavelength noon states by quantum frequency up-conversion, Phys. Rev. Appl. source

      Only the nonlinear-optics portion of the citing sentence is attributed to this source [73]. The paper’s experimental passages describe sum-frequency up-conversion and NOON-state phase measurements, but do not address whether nonlinear optics increases Bell-state discrimination success rates. A Bell-state measurement appears in the References, not as a finding of this paper. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [76] Kaltenbaek, 2006, Experimental interference of independent photons, Phys. Rev. Lett. source

      The Abstract reports interference between photons from independent sources, and the experimental description reports interference visibility, not Bell-state discrimination success rates. Searches for nonlinear optics, auxiliary-mode entanglement, and feed-forward techniques found no passage in our copy linking them to higher discrimination success rates. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Full device independent QKD allows security to be proven without any knowledge of the devices used in the implementation.

    “One such solution is known as the full device independent QKD [95,96], where the security can be proven without any knowledge of the devices used in the implementation.”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [95] Lettow, 2010, Quantum interference of tunably indistinguishable photons from remote organic molecules, Phys. Rev. Lett. source

      The paper’s Abstract describes an experiment on two-photon interference from remote organic molecules, not device-independent QKD. Searches for device-independent quantum key distribution, security without knowledge of devices, and related QKD terms found no passage addressing the claim. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
    • cites [96] Calsamiglia, 2001, Maximum efficiency of a linear-optical Bell-state analyzer, Appl. Phys. B source

      The Introduction and Conclusions discuss photonic Bell-state measurements and the efficiency of a linear-optical analyzer, not QKD security. Searches for device-independent QKD and security without knowledge of implementation devices found no passage addressing that claim. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Premisecitation

    QOCT was experimentally demonstrated, achieving an improvement in resolution by a factor of 5 compared to OCT.

    “Not long after its proposal, QOCT was experimentally demonstrated, achieving an improvement in resolution by a factor of 5 compared to OCT [25].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [25] Kok, 2007, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. source

      The Abstract and VI. OUTLOOK: BEYOND LINEAR OPTICS discuss experiments in linear optical quantum computing, not QOCT. Searches for QOCT, quantum optical coherence tomography, and the claimed fivefold resolution improvement found no passage in our copy addressing the claim; page numbers were unavailable. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Such bi-partite quantum walks can be used to perform quantum simulations.

    “can be used to perform quantum simulations [159,160]”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [159] O’brien, 2009, Photonic quantum technologies, Nat. Photon. source

      The Quantum information processing section (p. 2) discusses photonic quantum computing and optical networks, but not bipartite quantum walks or their use in quantum simulation. Searches for “quantum walks,” “bipartite quantum walk simulation,” and “quantum simulation” found no passage in our copy addressing that use. (LLM, conf=0.74)

      Experimental — accuracy not yet measured
    • cites [160] Wang, 2020, Integrated photonic quantum technologies, Nat. Photon. source

  • It may state two separate claims as one.

    Premisecitation

    Several specific quantum optical implementations rely on the HOM effect, including solving systems of linear equations, computation on encrypted data, computing discrete and fractional Fourier transform, and computations on a single spatial mode using temporal modes.

    “There are several examples of specific quantum optical implementations that rely on the HOM effect, to list a few: solving systems of linear equations [128,129], computation on encrypted data [130], computing discrete and fractional Fourier transform [131], and computations on a single spatial mode (using temporal modes) [132].”
    Quote in the paperNot a substantial claim4 of 4 sources checked
    • cites [128] Pirandola, 2015, High-rate measurement-device-independent quantum cryptography, Nat. Photon. source

      The Discussion (p. 5) describes a continuous-variable quantum cryptography protocol, and the experimental setup (p. 16) describes optical modes combined for a Bell measurement. Searches for single-spatial-mode computation and temporal modes found no passage addressing that cited part of the sentence or its claimed reliance on the HOM effect. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [129] Sasaki, 2014, Practical quantum key distribution protocol without monitoring signal disturbance, Nature source

      The Abstract describes a quantum key distribution protocol using laser pulse trains, and the practical-implementation description in Additional information describes interference between delayed pulses. Neither passage addresses the HOM effect or computations on a single spatial mode using temporal modes. Searches for HOM-based computation, linear equations, encrypted data, and Fourier transforms found no supporting passage in our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [130] Takesue, 2015, Experimental quantum key distribution without monitoring signal disturbance, Nat. Photon. source

      Citation [132] is attached to the example of computations on a single spatial mode using temporal modes. The experimental-setup passage describes temporally delayed interferometers for quantum key distribution, but does not address that computational implementation or its reliance on the HOM effect. Searches for single-spatial-mode computation and HOM-based temporal-mode computation found no supporting passage in our copy. (LLM, conf=0.75)

      Experimental — accuracy not yet measured
    • cites [131] Wang, 2015, Experimental demonstration of a quantum key distribution without signal disturbance monitoring, Nat. Photon. source

      The citation is attached to the claim about solving systems of linear equations. The paper’s discussion of its variable-delay interferometer for quantum key distribution does not address that computation or connect it to the HOM effect. Searches for linear equations and HOM interference found no supporting passage in our copy (page numbers unavailable). (LLM, conf=0.77)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Findingcitation

    Upon exiting the beam splitter, the symmetric component Ψ+ of the input state results in two photons being detected in one of the output ports, while the antisymmetric component Ψ− results in one photon being detected in each output port.

    “Upon exiting the beam splitter, the symmetric component, Ψ + i j , of the input state will reseult in two photons being detected in one of the output ports, while the antisymmetric component, Ψ - i j , will result in one photon being detected in each output port.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [111] Guan, 2015, Experimental passive round-robin differential phase-shift quantum key distribution, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Findingreasoning

    When the two photons exit through the same port in this cloning scheme, 2/3 of the time they will have the same polarization state, and 1/3 of the time they will have orthogonal polarization states.

    “When the two photons exit through the same port, 2/3 of the time they will have the same polarization state; while 1/3 of the time, they will have orthogonal polarization states, |1 s |1 s ⊥ .”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    For fermionic particles, the creation operators anti-commute, implying that ĉ† d† = -d† ĉ†, and fermions will exit through different output ports.

    “In the case of fermionic particles, say electrons, the creation operators will anti-commute, implying that ĉ † d † = -d † ĉ † . Therefore, |1 a |1 b BS -→ |1 c |1 d and the fermions will exit through different output ports.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Findingreasoning

    For indistinguishable photons incident on a 50:50 BS, destructive interference occurs for two-photon states corresponding to photons exiting opposite output ports, and constructive interference occurs for photons exiting through the same output ports.

    “In this case, we observe destructive interference of the two-photon states corresponding to photons exiting opposite output ports, and constructive interference of the two-photon states corresponding to photons exiting through the same output ports.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    For the Bell states |Φ±_ab after a beam splitter, both photons end up in the same detector with the same polarization.

    “in the last case they also reach the same detector, but they have the same polarizations”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Findingreasoning

    From Eq. (17), the probability for passing the SWAP test is (1 + |⟨φ|ψ⟩|^2)/2, and the probability of failing is (1 - |⟨φ|ψ⟩|^2)/2.

    “From Eq. ( 17), we can find the probability for passing the test is 1 + | φ| ψ | 2 /2, and consequently the probability of failing the test is 1 -| φ| ψ | 2 /2.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given

    Two-photon interference has no classical analogue.

    “two-photon interference has no classical analogue”
    • Also stated in: § I. INTRODUCTION · boosted
      “with absolutely no analogue in classical physics”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The HOM effect is fundamental to a plethora of quantum information tasks.

    “As will be discussed in the upcoming sections, the two-photon interference is fundamental to a plethora of quantum information tasks.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    The MDI QKD protocol has been experimentally demonstrated using time-bin phase encoding and polarization encoding.

    “The MDI QKD protocol has been experimentally demonstrated using time-bin phaseencoding [97], and polarization encoding [98].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [97] Kim, 2001, Quantum teleportation of a polarization state with a complete bell state measurement, Phys. Rev. Lett. source
    • cites [98] Kwiat, 1998, Embedded bell-state analysis, Phys. Rev. A source

  • Probably not a substantial claim.

    Premisenone given

    Quantum state joining requires a particle to have enough degrees of freedom to accommodate the information of both incoming states.

    “We thus require a particle to have enough degrees of freedom to accommodate the information of both incoming states.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    This quantum state joining process is probabilistic and requires an ancilla state, with a success probability of 1/32, or 1/8 if a suitable feed-forward is used.

    “This process is probabilistic and requires an ancilla state, with a success probability of 1/32, or 1/8 if a suitable feed-forward is used.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [120] Gerhardt, 2011, Full-field implementation of a perfect eavesdropper on a quantum cryptography system, Nat. Commun. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Interpretationreasoning

    The passive RRDPS QKD configuration typically yields larger security, better stability, and faster communications.

    “As a result, such a configuration typically yields larger security, better stability, and faster communications.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The experimental realization of indistinguishable single photon sources with high purity is a crucial component for engineering large-scale entangled quantum states from independent sources.

    “The experimental realization of indistinguishable single photon sources with high purity is a crucial component for engineering large-scale entangled quantum states from independent sources, as will be seen in forthcoming sections.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    The Heisenberg uncertainty principle and the no-cloning theorem are the basis of security when encoding information on single photons, because any type of eavesdropping results in disturbances of the photonic quantum states.

    “The Heisenberg uncertainty principle and the no-cloning theorem [79] are the basis of security when encoding information on single photons, since any type of eavesdropping results in disturbances of the photonic quantum states.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [79] Flagg, 2010, Interference of single photons from two separate semiconductor quantum dots, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    This quantum state joining scheme relies on the interaction of two photons, which would require nonlinear optics.

    “This scheme relies on the interaction of two photons, which would require nonlinear optics.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The inverse process to joining states, quantum state splitting, splits the information on a ququart state onto two photonic qubits.

    “The inverse process to joining states, known as quantum state splitting, is such that the information on a ququart state (for the above experiment) is split onto two photonic qubits [121].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [121] Mayers, 1998

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    MDI QKD still necessitates the assumptions that Alice's and Bob's state generation are perfect, which is still reasonable for current implementations.

    “In contrast to the full device independent scheme, MDI QKD protocol still necessitates the assumptions of Alice's and Bob's states generation to be perfect, which is still reasonable for current implementations.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The measurement of HOM visibility is an invaluable diagnostic tool to characterize single photon sources and states.

    “In particular, the measurement of the HOM visibility is an invaluable diagnostic tool to characterize single photon sources and states.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationnone given

    QOCT offers potential advantages in terms of resolution but new challenges appear, such as low signal and signal artifacts.

    “Finally, although QOCT offers potential advantages in terms of resolution, new challenges appear, such as low signal and signal artifacts.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationcitation

    If the maximally mixed polarization state is created by using one photon from a maximally entangled singlet state, then 2/3 of the time the other photon in the singlet state will have the orthogonal polarization of the cloned states, and 1/3 of the time the same polarization, effectively implementing an optimal universal NOT gate.

    “Suppose we created the maximally mixed polarization state by using one of the photons from a maximally entangled singlet state.Then 2/3 of the time, the other photon in the singlet state will have the orthogonal polarization of the cloned states, and 1/3 of the time the same polarization.This effectively implements an optimal universal NOT gate [118,119]-itself a non-unitary operation.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [118] Zhao, 2008, Quantum hacking: experimental demonstration of time-shift attack against practical quantum-key-distribution systems, Phys. Rev. A source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [119] Lydersen, 2010, Hacking commercial quantum cryptography systems by tailored bright illumination, Nat. Photon. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Quantum entanglement is the fundamental resource in quantum communication, quantum metrology, and quantum computing.

    “At the heart of quantum information is the notion of quantum entanglement [10]-the fundamental resource in quantum communication [11], quantum metrology [12], and quantum computing [13].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [10] Hamilton, 2000, Phase shifts in multilayer dielectric beam splitters, Am. J. Phys. source
    • cites [11] Paul, 1986, Interference between independent photons, Rev. Mod. Phys. source
    • cites [12] Ou, 1989, Fourth-order interference technique for determining the coherence time of a light beam, J. Opt. Soc. Am. B source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Universal quantum computation can be achieved with linear optics, post-selection, single photon sources and detectors, and feed-forward, as proposed by the KLM protocol.

    “Universal quantum computation can be achieved with linear optics, post-selection, single photon sources and detectors, and feed-forward, as was proposed by the KLM protocol [76].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [76] Kaltenbaek, 2006, Experimental interference of independent photons, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    To achieve optimal HOM interference, attenuated lasers are phase randomized, achieving a maximum HOM visibility of 1/2.

    “In order to achieve an optimal HOM interference, the attenuated lasers are phase randomized, achieving a maximum HOM visibility of 1/2.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisenone given

    The CZ and CNOT gates are main components for universal quantum computation.

    “Two such gates are the control-Z (CZ) and control-NOT (CNOT) gates, which are main components for universal quantum computation.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    Two-photon interference is one of the primary tools used in quantum information processing.

    “In addition to being one of the most peculiar phenomenon in quantum optics, two-photon interference is one of the primary tools used in quantum information processing.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    The last two Bell states |Φ± cannot be distinguished from each other with a simple pair of photon detectors, giving a success rate of 50%.

    “We cannot distinguish the last two states, |Φ ± , from each other with a simple pair of photon detectors; hence, the success rate of 50%.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Entanglement is a key physical principle at the heart of quantum communications.

    “Another key physical principle that is at the heart of quantum communications is entanglement [10].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [10] Hamilton, 2000, Phase shifts in multilayer dielectric beam splitters, Am. J. Phys. source

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    A beam splitter can be represented by a unitary transformation, thus conserving energy and preserving orthogonality between input states.

    “Formally, it can be represented by a unitary transformation, thus conserving energy and preserving orthogonality between input states.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The HOM effect is not limited to photons; it has implementations in non-photonic systems such as plasmons, phonons, atoms and electrons.

    “Of course, the HOM effect is not limited to photons, and thus we close the review with implementations in non-photonic systems, such as plasmons, phonons, atoms and electrons.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may state two separate claims as one.

    Interpretationnone given

    Two-photon interference and Bell state analysis are central concepts in MDI-QKD.

    “The two-photon interference and Bell state analysis are central concepts in MDI-QKD.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisereasoning

    In the passive RRDPS scheme, Bob generates a reference pulse train and sends Alice's and his state to a beam splitter, taking advantage of the phase stability of the two-photon interference effect.

    “Instead of measuring the interference of a train of pulses at Bob's stage, Bob generates a reference pulse train, and sends Alice's and his state to a beam splitter.By using such a configuration, Bob takes advantage of the phase stability of the twophoton interference effect.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    By arranging four beam splitters to interfere the original state with another entangled ancillary pair of modes first, and then sending each of the two pairs of output modes through a simple Bell state analyzer, one can distinguish one of the two previously indistinguishable states and raise the success rate to 75%.

    “As outlined in [77], an example can be to arrange four beam splitters so that we interfere the original state with another entangled ancillary pair of modes first, and then each of the two pairs of output modes goes through a simple Bell state analyzer.In this way, we can distinguish one of the two states that we could not distinguish before, raising the success rate to 75%.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [77] Mosley, 2008, Heralded generation of ultrafast single photons in pure quantum states, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    A heralded single photon source achieving unity HOM visibility would lead to a higher secret key rate per transmitted photon.

    “A heralded single photon source achieving a unity HOM visibility would lead to a higher secret key rate per transmitted photon.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    New techniques are being investigated to exploit the full potential of QOCT.

    “Thus, new techniques are being investigated in order to exploit the full potential of QOCT [29][30][31][32].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [29] Slussarenko, 2017, Unconditional violation of the shot-noise limit in photonic quantum metrology, Nat. Photon. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [30] D’Ambrosio, 2019, Tunable two-photon quantum interference of structured light, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [31] Hiekkamäki, 2020, Single-path two-photon interference effects between spatial modes source

  • It may state two separate claims as one.

    Premisecitation

    Two-photon interference has inherent dispersion cancellation, which does not occur in one-photon interference or classical light interference.

    “Another particularity of the two-photon interference is its inherent dispersion cancellation, which does not occur in the case of the one-photon interference, or the interference of classical light.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [22] Einstein, 1935, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Interpretationreasoning

    Two-photon interference gives a distinct advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements.

    “It is precisely this separation from classical to quantum physics that gives two-photon interference a distinct advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    The RRDPS protocol removes the requirement for signal disturbance monitoring by bounding the amount of information leaked to the eavesdropper, with the bound depending entirely on Alice's generation stage.

    “The RRDPS protocol removes the requirement for signal disturbance monitoring by bounding the amount of information leaked to the eavesdropper, where the bound depends entirely on Alice's generation stage.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [102] Gisin, 2002, Quantum cryptography, Rev. Mod. Phys. source

  • It may state two separate claims as one.

    Premisereasoning

    Full device independent QKD yields very low secret key rates and is highly impractical due to stringent requirements such as near unity detection efficiencies.

    “However, this scheme yields very low secret key rates, and is highly impractical due to several stringent requirements such as near unity detection efficiencies.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    The HOM effect might play an important role in the engineering and analysis of entangled states.

    “Quantum entanglement inherently deals with the interference of two-photon states, thus hinting to the fact that the HOM effect might play an important role in the engineering and analysis of entangled states.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Many quantum communication schemes, such as entanglement swapping, quantum teleportation, and dense-coding, are based on the concept of entanglement.

    “Beyond quantum cryptography, many quantum communication schemes-such as entanglement swapping [81], quantum teleportation [82], and dense-coding [83]-are also based on the concept of entanglement.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [81] Wei, 2014, Deterministic and robust generation of single photons from a single quantum dot with 99.5% indistinguishability using adiabatic rapid passage, Nano Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [82] Senellart, 2017, High-performance semiconductor quantum-dot single-photon sources, Nat. Nanotechnol. source
    • cites [83] Felinto, 2006, Conditional control of the quantum states of remote atomic memories for quantum networking, Nat. Phys. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    The two-way architecture for quantum repeaters works by having quantum memories evenly distributed along a communication channel, each memory hosting two atoms that emit photons forwards and backwards, with a Bell state analyzer midway between two memories measuring the two photons in the Bell basis.

    “the so-called “two-way architecture” works by having quantum memories evenly distributed along a communication channel, each memory hosting two atoms that emit photons as described above, one forwards and one backwards along the channel.Mid-way between two memories M 1 M 2 sits a Bell state analyzer that measures the two photons coming from M 1 and M 2 in the Bell basis.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [89] Sipahigil, 2012, Quantum interference of single photons from remote nitrogen-vacancy centers in diamond, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Interpretationcitation

    The entangled state of two atoms created by this procedure will display non-local correlations, verifiable by violating Bell's inequalities.

    “We have thus created an entangled state of two atoms, which will display non-local correlations as one can verify for example by violating Bell's inequalities [87].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [87] Chen, 2008, Memory-built-in quantum teleportation with photonic and atomic qubits, Nat. Phys. source

  • It may state two separate claims as one.

    Premisereasoning

    The issue of random detection time difference in entangling photons with different frequencies can be solved either by postselecting on measurements within a very narrow time window, or by recording the time difference and feed-forwarding a phase correction so that every single photon pair will have the same phase.

    “However, one can solve this issue either by postselecting on only the measurements that fall within a very narrow time window (but this reduces the total number of successful measurements), or by recording the time difference and feed-forward a phase correction so that every single photon pair will have the same phase.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Bunching and anti-bunching are typical bosonic and fermionic behaviours, respectively.

    “Interestingly, bunching and anti-bunching are typical bosonic and fermionic behaviours, respectively.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14] Kim, 2014, Two-photon interference with continuous-wave multi-mode coherent light, Opt. Express source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    The frequency difference ∆ω between photons from different-frequency pairs generates a phase exp(i∆ω∆t) between the components, which will render the state mixed if unaccounted for because the detection time difference ∆t is random.

    “The frequency difference ∆ω generates a phase of exp(i∆ω∆t) between the components, which will render the state mixed if unaccounted for because the detection time difference ∆t is random.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [112] Hofmann, 2012, Heralded entanglement between widely separated atoms, Science source

  • It may state two separate claims as one.

    Premisecitation

    The MDI scheme has been demonstrated over long distances through optical fibres, showing feasibility and potential for unconditional security.

    “Moreover, the MDI scheme has also been demonstrated over long distances through optical fibres [99,100], showing the feasibility of the protocol and its potential for unconditional security.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [99] Barreiro, 2008, Beating the channel capacity limit for linear photonic superdense coding, Nat. Phys. source
    • cites [100] Knill, 2001, A scheme for efficient quantum computation with linear optics, Nature source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    Bell state measurements are the gold standard for experimentally measuring maximally entangled states.

    “Furthermore, Bell state measurements are the gold standard for experimentally measuring maximally entangled states.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationnone given

    In all boson sampling tasks, multi-photon as well as multimodal interferences play a crucial role.

    “in all boson sampling tasks, multi-photon as well as multimodal interferences, i.e. generalizations of the original HOM idea, play a crucial role.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    A probability surface or coincidence landscape is useful to probe indistinguishability or to predict the complex device's quantum behaviour.

    “which is useful to probe indistinguishability or to predict the complex device's quantum behaviour [163].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [163] Reck, 1994, Experimental realization of any discrete unitary operator, Phys. Rev. Lett. source

  • It may state two separate claims as one.

    Premisereasoning

    For the two-dimensional case, a Bell state measurement can be implemented with a single beamsplitter followed by a detector in each output port, which is equivalent to a destructive SWAP test in the sense that the states get measured and are not available afterwards.

    “For the two-dimensional case, we can implement a Bell state measurement with a single beamsplitter followed by a detector in each output port, which is equivalent to a destructive SWAP test in the sense that the states get measured and are not available afterwards.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    In the 4He BEC experiment, the cross-correlation measurements showed a clear dip with visibility 0.65±0.07, above the classical limit of 0.5.

    “the results show a clear dip in the cross-correlation measurements with a visibility of 0.65±0.07,which is above the classical limit of 0.5”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [193] Tichy, 2013, Limits to multipartite entanglement generation with bosons and fermions, Phys. Rev. A source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    In plasmonic systems, usually deleterious losses might be turned into an advantageous feature when the nanostructures are carefully tuned.

    “it was shown that the usually deleterious losses associated with plasmonic systems might be turned into a advantageous feature when the nanostructures are carefully tuned.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [187] Crespi, 2013, Anderson localization of entangled photons in an integrated quantum walk, Nat. Photon. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    Because the initial findings used a continuous stream of electrons, the interference might not exclusively be interpreted as a result from the overlap between two single-electron wave packets.

    “because these initial findings used a continuous stream of electrons, the interference might not exclusively be interpreted as a result from the overlap between two single-electron wave packets.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Due to anti-bunching, a reduction in the noise properties of the output ports was observed, providing an indirect verification of two-electron antibunching.

    “Due to anti-bunching, a reduction in the noise properties of the output ports was observed; thus, an indirect verification of two-electron antibunching was achieved.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [196] Broome, 2013, Photonic boson sampling in a tunable circuit, Science source
    • Rests on an assumption: Fermions obey Fermi statistics, which leads to anti-bunching at a beam splitter.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisenone given

    The HOM effect is colloquially referred to as a test for the distinguishability between two photons: if we witness a coincidence, the two photons had different states.

    “The Hong-Ou-Mandel effect is colloquially referred to as a test for the distinguishability between two photons: if we witness a coincidence, the two photons had different states.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    The CZ gate heavily relies on the HOM effect, with the output depending on whether the control and target photons bunched or not.

    “Overall, we see that the CZ gate heavily relies on the HOM effect, the output depending on whether the control and target photons bunched or not.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim.

    Interpretationreasoning

    The phonon experiment opens the path to phonon quantum information experiments relying on phononic HOM interference.

    “the experiment opens the path to phonon quantum information experiments, such as boson sampling or entanglement generation in larger ion crystals, relying on a phononic HOM interference.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Such bi-partite quantum walks give rise to interesting quantum correlation patterns.

    “that gives rise to interesting quantum correlation patterns [157,158]”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [157] Weimann, 2016, Implementation of quantum and classical discrete fractional fourier transforms, Nat. Commun. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [158] Humphreys, 2013, Linear optical quantum computing in a single spatial mode, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    The observed plasmonic HOM dip had a visibility of 0.43±0.02, below the classical limit of 0.5.

    “Although the observed dip had only a visibility of 0.43±0.02(see Fig. 8b) and thus below the classical limit of 0.5”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [180] Lahini, 2012, Quantum walk of two interacting bosons, Phys. Rev. A source

  • It may state two separate claims as one.

    Interpretationcitation

    By making the photons pairwise distinguishable, e.g. by delaying independently two photons, one can map a probability surface with non-trivial features, which can be seen as the three-dimensional extension to the 2-dimensional HOM interference dip.

    “By making the photons pairwise distinguishable, e.g. by delaying independently two photons, one can map a probability surface with non-trivial features (see Fig. 7b).This surface can be seen as the three-dimensional extension to the 2-dimensional HOM interference dip [141].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [141] Navez, 2003, Cloning a real d-dimensional quantum state on the edge of the no-signaling condition, Phys. Rev. A source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The complex features of three-partite interference experiments were also discussed in terms of quantum metrology and phase sensing to enhance precision.

    “Importantly, the complex features of three-partite interference experiments were also discussed in terms of quantum metrology and phase sensing to enhance precision [145].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [145] Ricci, 2004, Teleportation scheme implementing the universal optical quantum cloning machine and the universal not gate, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    At the plasmonic beam splitter, anti-coalescence or non-linear absorption can be observed.

    “At the plasmonics beam splitter, anti-coalescence or non-linear absorption can be observed [187].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [187] Crespi, 2013, Anderson localization of entangled photons in an integrated quantum walk, Nat. Photon. source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Such bi-partite quantum walks can probe the statistics in quantum walks.

    “or can probe the statistics in quantum walks [161].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [161] Garcia-Escartin, 2013, Swap test and Hong–Ou–Mandel effect are equivalent, Phys. Rev. A source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisereasoning

    For two maximally distinguishable (orthogonal) states, the overlap is 0 and the pass probability is 1/2, while for maximally indistinguishable states the overlap is 1 and the probability to pass the test is also 1.

    “For two maximally distinguishable (orthogonal) states, the overlap is 0 and P = 1/2, while for maximally indistinguishable states the overlap is 1 and the probability to pass the test is also 1.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Two-plasmon HOM interference is well-established and can be considered one of the building blocks of future quantum plasmonic circuits.

    “Since two plasmon HOM interference is now well-established, it can be considered one of the building blocks of future quantum plasmonic circuits”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    The triad phase is the sum of the three relative phases between pairwise inputs and only affects the outcome if the photons are partially distinguishable.

    “This so-called triad phase is the sum of the three relative phases between pairwise inputs (see Fig. 7c) and only effects the outcome if the photons are partially distinguishable.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    In higher dimensions, one needs the equivalent circuit for projecting onto the symmetric/antisymmetric subspaces.

    “In higher dimensions, one needs the equivalent circuit for projecting onto the symmetric/antisymmetric subspaces.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim.

    Premisenone given

    The SWAP test is a quantum computing primitive operation that tests for the inequality between two quantum states.

    “Similarly, the SWAP test is a quantum computing primitive operation that tests for the inequality between two quantum states.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Bell-ports have been discussed theoretically for many years in connection to multipartite and high-dimensional quantum information.

    “Bell-ports have been discussed theoretically since many years in connection to multipartite and high-dimensional quantum information [137,139,140].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [137] Jamiolkowski, 1972, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. source
    • cites [139] Zhao, 2014, Entangling different-color photons via time-resolved measurement and active feed forward, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [140] Peres, 2003, How the no-cloning theorem got its name, Fortschr. Phys. source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisereasoning

    In the SWAP test, if the outcome is |'1', the two input states are different; if the outcome is |'0', they may or may not be equal.

    “In terms of the measurement outcome, if |'1' is measured, we can confirm that the two input states are different; however, if the outcome is the state |'0' , they may or may not be equal.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Variations of the NS gate have been reported: one proposal using only two beam splitters but with a slightly lower success probability of (3 - √2)/7; other schemes with two ancillary photons with success probabilities 1/5 and 1/4.

    “Variations of the NS gate have been reported: one proposal shows the possibility to implement it using only two BS but with slightly lower success probability of (3 -√ 2)/7 [123]; other schemes with again two ancillary photons with success probabilities 1/5 [124] and 1/4 [125].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [123] Liu, 2013, Experimental measurement-device-independent quantum key distribution, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [124] Tang, 2014, Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [125] Tang, 2014, Measurement-device-independent quantum key distribution over 200 km, Phys. Rev. Lett. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    Waveguides in photonics chips allow for higher portability, higher cost efficiency, and higher robustness.

    “Waveguides in photonics chips allow for higher portability, higher cost efficiency, and higher robustness [133,134].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [133] Yin, 2018, Improved security bound for the round-robin-differential-phase-shift quantum key distribution, Nat. Commun. source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [134] Bouchard, 2018, Round-robin differential-phase-shift quantum key distribution with twisted photons, Phys. Rev. A source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisereasoning

    Boson sampling challenges the extended Church-Turing thesis.

    “In addition, it is also suggested that this challenges a fundamental principle of computer science, namely the extended Church-Turing thesis.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [166] Żukowski, 1997, Realizable higher-dimensional two-particle entanglements via multiport beam splitters, Phys. Rev. A source
    • cites [167] Campos, 2000, Three-photon Hong–Ou–Mandel interference at a multiport mixer, Phys. Rev. A source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    If more than two photons are interfered, a probability surface or coincidence landscape can be investigated.

    “if more than two photons are interfered, a probability surface or coincidence landscape can be investigated [162]”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [162] Zeilinger, 1993, Einstein–Podolsky–Rosen correlations in higher dimensions

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisereasoning

    Boson sampling is considered a promising candidate to show quantum supremacy.

    “and as such it is considered to be a promising candidate to show quantum supremacy.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [166] Żukowski, 1997, Realizable higher-dimensional two-particle entanglements via multiport beam splitters, Phys. Rev. A source
    • cites [167] Campos, 2000, Three-photon Hong–Ou–Mandel interference at a multiport mixer, Phys. Rev. A source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    When two particles are sent into a multiport, the transmission can be described as a complex bi-partite quantum walk.

    “When two particles for example are sent into a multiport, e.g.multimode waveguide [153,154], multimode fiber [155] or integrated waveguide structures [156], the transmission can be described as a complex bi-partite quantum walk”
    Quote in the paperNot a substantial claim0 of 4 sources checked
    • cites [153] Okamoto, 2011, Realization of a Knill–Laflamme–Milburn controlled-not photonic quantum circuit combining effective optical nonlinearities, Proc. Natl Acad. Sci. source
    • cites [154] Harrow, 2009, Quantum algorithm for linear systems of equations, Phys. Rev. Lett. source
    • cites [155] Cai, 2013, Experimental quantum computing to solve systems of linear equations, Phys. Rev. Lett. source
    • cites [156] Fisher, 2014, Quantum computing on encrypted data, Nat. Commun. source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    The eigenstates of the SWAP operator are the Bell states: three Bell states correspond to eigenvalue +1 (the symmetric subspace), and one corresponds to eigenvalue -1 (the singlet state, i.e. the antisymmetric subspace).

    “The eigenstates of the SWAP operator are the Bell states: three Bell states correspond to the eigenvalue +1 (the symmetric subspace), and one corresponds to the eigenvalue -1 (the singlet state, i.e. the antisymmetric subspace).”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    The triad phase leads to a change in detection probabilities when all three photons are detected in separate output ports and does not affect bi-photon transmission probabilities.

    “It leads to a change in the detection probabilities when all three photons are detected in separate output ports and does not affect the bi-photon transmission probabilities.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

  • It may state two separate claims as one.

    Premisecitation

    Levitons have been observed and brought to two-fermionic quantum interference only recently.

    “they have been observed and even brought to twofermionic quantum interference only recently [201].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [201] Bentivegna, 2015, Experimental scattershot boson sampling, Sci. Adv. source

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    In quantum computation, the interaction between two photons is often required to create building blocks of certain quantum gates, e.g. CNOT and CZ gates.

    “In quantum computation, the interaction between two photons is often required to create the building blocks of certain quantum gates, for example CNOT and CZ gates.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Premisenone given

    Two-photon interference enables the measurement of maximally entangled states through Bell state measurements.

    “two-photon interference enables the measurement of maximally entangled states through Bell states measurements, or equivalently, the projection onto the Bell basis.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given

    Two-photon interference has no classical counterpart.

    “Two-photon interference is fundamentally interesting because it has no classical counterpart”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Interpretationnone given

    In quantum communication, two-photon interference can be used to circumvent the problem of untrusted measurement devices and build novel protocols.

    “In quantum communication, it can be used to circumvent the problem of untrusted measurement devices, and build novel protocols.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given

    In quantum state analysis, two-photon interference gives the possibility to distinguish between modes, since only indistinguishable states will bunch.

    “In quantum state analysis, it gives the possibility to distinguish between modes, since only indistinguishable states will bunch.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    Two-photon interference has many applications ranging from precision measurement and state determination to quantum computations and quantum communication.

    “with many applications ranging from precision measurement and state determination to quantum computations and quantum communication.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    In metrology, two-photon interference allows for femtosecond and even attosecond time-resolution, state determination, and generating non-classical light for resolution enhancement with linear optics.

    “In metrology, two photon interference allows for femtosecond and even attosecond time-resolution, state determination (quantum state analysis), and generating non-classical light for resolution enhancement with linear optics.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Interpretationreasoning

    Two-photon interference acts as the linear optical solution to this challenge and provides a scalable technique to build photonic quantum computers.

    “Two-photon interference acts as the linear optical solution to this challenge, and thus provides a scalable technique to build photonic quantum computers.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationnone given

    Two-particle interferences is the basis for most optical quantum information science and a powerful tool for metrology and other fields.

    “Two particle interferences is not only the basis for most of optical quantum information science and a powerful tool for metrology and other fields”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    Bell state measurements are central to teleportation and entanglement swapping.

    “Bell state measurements are central to the concepts of teleportation and entanglement swapping.”
    Quote in the paperNot a substantial claim
97 of 97

  • The paper relies on this without support.

    Fermions obey Fermi statistics, which leads to anti-bunching at a beam splitter.

    “The major difference between indistinguishable bosons and fermions is that the latter obey Fermi statistics, which leads to anti-bunching at a beam splitter.”

  • The paper relies on this without support.

    SPPs, being bosonic quasiparticles, are expected to bunch in a HOM-type experiment.

    “Because SPPs are described as quasiparticles with a bosonic nature, they were also expected to bunch in a HOM-type experiment.”

  • The paper relies on this without support.

    Phonons follow Bose-Einstein statistics and are expected to bunch in a HOM-like arrangement.

    “Phonons also follow Bose-Einstein statistics, and as such they are expected to bunch in a HOM-like arrangement.”

  • The paper relies on this without support.

    Even massive particles should be able to exhibit two-particle interferences following quantum mechanics.

    “following quantum mechanics, even massive particles should be able to exhibit two-particle interferences.”
4 of 4

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • The state-joining expansion swaps its two cross terms

    Minor

    Expanding the tensor product gives αδ for a horizontally polarized photon in mode I and a vertically polarized photon in mode II, and βγ for the reverse. The displayed expansion assigns those coefficients the other way around.

  • The two-photon N00N state is attributed to the wrong equation

    Minor

    The paper says the N = 2 N00N state is the state in Eq. (5), but Eq. (5) defines polarization Bell states with one photon in each input path. The two-photon path N00N state produced by the beam splitter is instead displayed in Eq. (4).

2 of 2

Citations

Cites

Flagged first, then by citations

3 of the 257 references couldn’t be matched to a known paper.

Cited by

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Related

Metadata

Authors
Bouchard, F., Sit, A., Zhang, Y., Fickler, R., Miatto, F. M., Yao, Y., Sciarrino, F., & Karimi, E.
Affiliations
  • University of Ottawa (CA)
  • National Research Council Canada (CA)
  • Télécom Paris (FR)
  • Sapienza University of Rome (IT)
Corresponding author
Karimi, Ebrahim
ORCID
Venue
Reports on Progress in Physics
Publisher
IOP Publishing
Published
2020-12-24
Volume
84
Issue
1
Pages
012402
ISSN
  • 0034-4885 (ISSN-L)
  • 1361-6633
DOI
10.1088/1361-6633/abcd7a
OpenAlex
W3034980548
Semantic Scholar
93d14a8357b5c60331f7ab0d5939307953fa1e08
Cited by
232
References
257
Citations by year
2026: 48 · 2025: 50 · 2024: 40 · 2023: 51 · 2022: 31 · 2021: 12
FWCI
9.61
Type
journal article
Language
en
Open access
Licence
Locations
  • Reports on Progress in Physics (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • NPARC (submittedVersion)
  • Figshare (submittedVersion, cc-by)
  • arXiv (Cornell University)
Funders
  • Ontario Early Researcher Award
  • Canada Research Chairs
  • Canada First Research Excellence Fund
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
Keywords
two-photon interference, Hong-Ou-Mandel interference, two-particle interference, quantum optics, massive particles, electrons, atoms, plasmons, quantum computing, quantum communication, quantum simulation, precision measurement

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

A language model drew the claims from the paper on 2026-11-10, under version 3 of the claim definition (model deepseek-v4.1-flash, prompt extract-v3).

A second model labelled each claim on 2026-11-10 (model jev-1.13-20260917, definition revision gold-guideline-v0.2).

Cited sources are checked with a language model’s help (gpt-6-sol).

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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