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

In the paper

“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.”

What the sources say

• ?Not checked — no full text of the sourcecites [183] Politi, 2009, Integrated quantum photonics, IEEE J. Select. Top. Quantum Electron. source
• Partly supported

  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)

  cites [184] Peruzzo, 2010, Quantum walks of correlated photons, Science sourceExperimental — accuracy not yet measured
• Partly supported

  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)

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

  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.

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

In the paper

“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].”

What the sources say

• Partly supported

  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)

  cites [138] Zhang, 2016, Engineering two-photon high-dimensional states through quantum interference, Sci. Adv. sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

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

  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.

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

  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)

  cites [141] Navez, 2003, Cloning a real d-dimensional quantum state on the edge of the no-signaling condition, Phys. Rev. A sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

In the paper

“They have also been experimentally realized with fused optical fibers [138] and more recently with passive [141] and active integrated waveguide circuits [142].”

What the sources say

• Disputed

  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.

  cites [138] Zhang, 2016, Engineering two-photon high-dimensional states through quantum interference, Sci. Adv. sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

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

  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)

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

In the paper

“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.”

What the sources say

• ?Could not verify

  The supplied passages and searches for the Heisenberg uncertainty principle, no-cloning, and eavesdropping discuss single-photon interference and quantum-information applications, but not security from eavesdropping. Our copy therefore does not address the claim attributed to this paper (passages labeled Abstract; page unavailable). (LLM, conf=0.77)

  cites [79] Flagg, 2010, Interference of single photons from two separate semiconductor quantum dots, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Higher success rates can be achieved with nonlinear optics [73], entanglement in auxiliary modes [74,75], or feed-forward techniques [76].”

What the sources say

• ?Could not verify

  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)

  cites [73] Nagata, 2007, Beating the standard quantum limit with four-entangled photons, Science sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [74] Afek, 2010, High-N00N states by mixing quantum and classical light, Science source
• ?Could not verify

  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)

  cites [75] Zhou, 2017, Superresolving phase measurement with short-wavelength noon states by quantum frequency up-conversion, Phys. Rev. Appl. sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

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

In the paper

“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.”

What the sources say

• Partly supported

  The passage following Eq. (3) (indexed under Abstract; page unavailable) says that equal pulse phases produce two clicks at the same detector, while different phases produce clicks at different detectors. The copy does not identify those cases as the symmetric Ψ+ and antisymmetric Ψ− components of the input state, so that identification is not established by this source. (LLM, conf=0.82)

  cites [111] Guan, 2015, Experimental passive round-robin differential phase-shift quantum key distribution, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“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.”

What the sources say

• ?Could not verify

  Section 2 discusses measurements and wave functions of two systems, not photon interference. Searches for two-photon interference and dispersion cancellation found no passage addressing either the claimed effect or its comparison with one-photon and classical-light interference. (LLM, conf=0.78)

  cites [22] Einstein, 1935, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. sourceExperimental — accuracy not yet measured

In the paper

“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.”

What the sources say

• ?Could not verify

  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)

  cites [95] Lettow, 2010, Quantum interference of tunably indistinguishable photons from remote organic molecules, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

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

In the paper

“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.”

What the sources say

• Partly supported

  The introduction (p. 1) identifies quantum teleportation as an example of photonic quantum information processing, and the conclusion (p. 4) discusses generating entangled photons. Our copy does not say that teleportation depends on entanglement or address entanglement swapping or dense-coding, so it supports only part of the attributed statement. (LLM, conf=0.77)

  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. sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites [82] Senellart, 2017, High-performance semiconductor quantum-dot single-photon sources, Nat. Nanotechnol. source
• Supported

  The citation [81] is attached specifically to entanglement swapping, not to teleportation or dense coding. The paper’s opening discussion states that quantum repeaters distribute entanglement by swapping across a chain of entangled pairs (page not supplied). (LLM, conf=0.93)

  cites [83] Felinto, 2006, Conditional control of the quantum states of remote atomic memories for quantum networking, Nat. Phys. source

In the paper

“Not long after its proposal, QOCT was experimentally demonstrated, achieving an improvement in resolution by a factor of 5 compared to OCT [25].”

What the sources say

• ?Could not verify

  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)

  cites [25] Kok, 2007, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys. sourceExperimental — accuracy not yet measured

In the paper

“can be used to perform quantum simulations [159,160]”

What the sources say

• ?Could not verify

  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)

  cites [159] O’brien, 2009, Photonic quantum technologies, Nat. Photon. sourceExperimental — accuracy not yet measured
• Supported

  The section “On-chip sampling of photons and quantum simulation” (p. 6) says quantum walks can serve as a resource for quantum simulations and describes two-particle quantum walks used to study physical phenomena. The Fig. 5 caption (p. 12) likewise identifies two-particle quantum walks as simulations of physical quantum phenomena. (LLM, conf=0.87)

  cites [160] Wang, 2020, Integrated photonic quantum technologies, Nat. Photon. source

In the paper

“that gives rise to interesting quantum correlation patterns [157,158]”

What the sources say

• Supported

  The Results section (Quantum experiments; page not available in our copy) describes pairs of photons propagating through waveguide arrays and reports distinct two-photon correlation patterns, including a rotated correlation map for path-entangled states. This supports the cited statement about correlation patterns arising from two-particle quantum propagation. (LLM, conf=0.88)

  cites [157] Weimann, 2016, Implementation of quantum and classical discrete fractional fourier transforms, Nat. Commun. source
• ?Could not verify

  The passage labeled Abstract mentions a classical simulation of a quantum random walk, but says nothing about bipartite walks producing quantum correlation patterns. The gate-operation and two-photon passages concern a CPhase gate, not walk-generated correlations. Searches for bipartite quantum walks and two-photon walk correlations found no passage addressing the claim; page numbers are unavailable in our copy. (LLM, conf=0.76)

  cites [158] Humphreys, 2013, Linear optical quantum computing in a single spatial mode, Phys. Rev. Lett. sourceExperimental — accuracy not yet measured

In the paper

“Waveguides in photonics chips allow for higher portability, higher cost efficiency, and higher robustness [133,134].”

What the sources say

• ?Could not verify

  The Results section (Proof-of-principle experiment; page unavailable) discusses beam splitters, Faraday–Michelson interferometers, and detector performance. Although it describes the interferometers as stable against polarization variations, our copy does not address whether waveguides in photonic chips improve portability, cost efficiency, or robustness. Searches for photonic-chip waveguides and related terms found no supporting passage. (LLM, conf=0.78)

  cites [133] Yin, 2018, Improved security bound for the round-robin-differential-phase-shift quantum key distribution, Nat. Commun. sourceExperimental — accuracy not yet measured
• ?Could not verify

  The paper’s body text, indexed under Abstract (page unavailable), discusses orbital-angular-momentum QKD and says its generation and detection techniques do not require active stabilization. It does not address whether waveguides in photonic chips improve portability, cost efficiency, or robustness; searches for waveguides, integrated photonics, and those claimed benefits found no relevant passage. (LLM, conf=0.75)

  cites [134] Bouchard, 2018, Round-robin differential-phase-shift quantum key distribution with twisted photons, Phys. Rev. A sourceExperimental — accuracy not yet measured

In the paper

“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].”

What the sources say

• ?Could not verify

  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)

  cites [128] Pirandola, 2015, High-rate measurement-device-independent quantum cryptography, Nat. Photon. sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

  cites [129] Sasaki, 2014, Practical quantum key distribution protocol without monitoring signal disturbance, Nature sourceExperimental — accuracy not yet measured
• ?Could not verify

  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)

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

  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)

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

In the paper

“they have been observed and even brought to twofermionic quantum interference only recently [201].”

What the sources say

• ?Could not verify

  The Introduction discusses interference of indistinguishable photons in boson sampling, not levitons. Searches of our copy for levitons and two-fermion interference found no passage addressing their observation or interference; the returned References also concern photons. Page numbers were not available. (LLM, conf=0.76)

  cites [201] Bentivegna, 2015, Experimental scattershot boson sampling, Sci. Adv. sourceExperimental — accuracy not yet measured

In the paper

“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 ⊥ .”

In the paper

“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.”

In the paper

“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.”

In the paper

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

In the paper

“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.”

In the paper

“two-photon interference has no classical analogue”

• Also stated in: § I. INTRODUCTION · boosted

  “with absolutely no analogue in classical physics”

In the paper

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

In the paper

“The MDI QKD protocol has been experimentally demonstrated using time-bin phaseencoding [97], and polarization encoding [98].”

What the sources say

• ?Not checked — no full text of the sourcecites [97] Kim, 2001, Quantum teleportation of a polarization state with a complete bell state measurement, Phys. Rev. Lett. source
• ?Not checked — no full text of the sourcecites [98] Kwiat, 1998, Embedded bell-state analysis, Phys. Rev. A source

In the paper

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

In the paper

“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.”

What the sources say

• Not checked yet

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

  cites [120] Gerhardt, 2011, Full-field implementation of a perfect eavesdropper on a quantum cryptography system, Nat. Commun. source

In the paper

“As a result, such a configuration typically yields larger security, better stability, and faster communications.”

In the paper

“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.”

In the paper

“This scheme relies on the interaction of two photons, which would require nonlinear optics.”

In the paper

“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].”

What the sources say

• ?Not matched

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

  cites [121] Mayers, 1998

In the paper

“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.”

In the paper

“In particular, the measurement of the HOM visibility is an invaluable diagnostic tool to characterize single photon sources and states.”

In the paper

“Finally, although QOCT offers potential advantages in terms of resolution, new challenges appear, such as low signal and signal artifacts.”

In the paper

“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.”

What the sources say

• Not checked yet

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

  cites [118] Zhao, 2008, Quantum hacking: experimental demonstration of time-shift attack against practical quantum-key-distribution systems, Phys. Rev. A source
• Not checked yet

  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

In the paper

“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].”

What the sources say

• ?Not checked — no full text of the sourcecites [10] Hamilton, 2000, Phase shifts in multilayer dielectric beam splitters, Am. J. Phys. source
• ?Not checked — no full text of the sourcecites [11] Paul, 1986, Interference between independent photons, Rev. Mod. Phys. source
• ?Not checked — no full text of the sourcecites [12] Ou, 1989, Fourth-order interference technique for determining the coherence time of a light beam, J. Opt. Soc. Am. B source

In the paper

“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].”

What the sources say

• Not checked yet

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

  cites [76] Kaltenbaek, 2006, Experimental interference of independent photons, Phys. Rev. Lett. source

In the paper

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

In the paper

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

In the paper

“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.”

In the paper

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

In the paper

“Another key physical principle that is at the heart of quantum communications is entanglement [10].”

What the sources say

• ?Not checked — no full text of the sourcecites [10] Hamilton, 2000, Phase shifts in multilayer dielectric beam splitters, Am. J. Phys. source

In the paper

“Formally, it can be represented by a unitary transformation, thus conserving energy and preserving orthogonality between input states.”

In the paper

“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.”

In the paper

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

In the paper

“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.”

In the paper

“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%.”

What the sources say

• Not checked yet

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

  cites [77] Mosley, 2008, Heralded generation of ultrafast single photons in pure quantum states, Phys. Rev. Lett. source

In the paper

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

In the paper

“Thus, new techniques are being investigated in order to exploit the full potential of QOCT [29][30][31][32].”

What the sources say

• Not checked yet

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

  cites [29] Slussarenko, 2017, Unconditional violation of the shot-noise limit in photonic quantum metrology, Nat. Photon. source
• Not checked yet

  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
• ?Not checked — no full text of the sourcecites [31] Hiekkamäki, 2020, Single-path two-photon interference effects between spatial modes source

In the paper

“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.”

In the paper

“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.”

What the sources say

• Not checked yetcites [102] Gisin, 2002, Quantum cryptography, Rev. Mod. Phys. source

In the paper

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

In the paper

“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.”

In the paper

“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.”

What the sources say

• Not checked yet

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

  cites [89] Sipahigil, 2012, Quantum interference of single photons from remote nitrogen-vacancy centers in diamond, Phys. Rev. Lett. source

In the paper

“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].”

What the sources say

• Not checked yetcites [87] Chen, 2008, Memory-built-in quantum teleportation with photonic and atomic qubits, Nat. Phys. source

In the paper

“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.”

In the paper

“Interestingly, bunching and anti-bunching are typical bosonic and fermionic behaviours, respectively.”

What the sources say

• Not checked yet

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

  cites [14] Kim, 2014, Two-photon interference with continuous-wave multi-mode coherent light, Opt. Express source

In the paper

“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.”

What the sources say

• ?Not checked — no full text of the sourcecites [112] Hofmann, 2012, Heralded entanglement between widely separated atoms, Science source

In the paper

“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.”

What the sources say

• ?Not checked — no full text of the sourcecites [99] Barreiro, 2008, Beating the channel capacity limit for linear photonic superdense coding, Nat. Phys. source
• ?Not checked — no full text of the sourcecites [100] Knill, 2001, A scheme for efficient quantum computation with linear optics, Nature source

In the paper

“Furthermore, Bell state measurements are the gold standard for experimentally measuring maximally entangled states.”

In the paper

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

In the paper

“which is useful to probe indistinguishability or to predict the complex device's quantum behaviour [163].”

What the sources say

• ?Not checked — no full text of the sourcecites [163] Reck, 1994, Experimental realization of any discrete unitary operator, Phys. Rev. Lett. source

In the paper

“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.”

In the paper

“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”

What the sources say

• Not checked yet

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

  cites [193] Tichy, 2013, Limits to multipartite entanglement generation with bosons and fermions, Phys. Rev. A source

In the paper

“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.”

What the sources say

• Not checked yetcites [187] Crespi, 2013, Anderson localization of entangled photons in an integrated quantum walk, Nat. Photon. source

In the paper

“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.”

In the paper

“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.”

What the sources say

• Not checked yetcites [196] Broome, 2013, Photonic boson sampling in a tunable circuit, Science source

In the paper

“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.”

In the paper

“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.”

In the paper

“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.”

In the paper

“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”

What the sources say

• Not checked yetcites [180] Lahini, 2012, Quantum walk of two interacting bosons, Phys. Rev. A source

In the paper

“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].”

What the sources say

• Not checked yet

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

  cites [141] Navez, 2003, Cloning a real d-dimensional quantum state on the edge of the no-signaling condition, Phys. Rev. A source

In the paper

“Importantly, the complex features of three-partite interference experiments were also discussed in terms of quantum metrology and phase sensing to enhance precision [145].”

What the sources say

• Not checked yet

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

  cites [145] Ricci, 2004, Teleportation scheme implementing the universal optical quantum cloning machine and the universal not gate, Phys. Rev. Lett. source

In the paper

“At the plasmonics beam splitter, anti-coalescence or non-linear absorption can be observed [187].”

What the sources say

• Not checked yetcites [187] Crespi, 2013, Anderson localization of entangled photons in an integrated quantum walk, Nat. Photon. source

In the paper

“or can probe the statistics in quantum walks [161].”

What the sources say

• Not checked yet

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

  cites [161] Garcia-Escartin, 2013, Swap test and Hong–Ou–Mandel effect are equivalent, Phys. Rev. A source

In the paper

“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.”

In the paper

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

In the paper

“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.”

What the sources say

• ?Not checked — no full text of the sourcecites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

In the paper

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

In the paper

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

In the paper

“Bell-ports have been discussed theoretically since many years in connection to multipartite and high-dimensional quantum information [137,139,140].”

What the sources say

• ?Not checked — no full text of the sourcecites [137] Jamiolkowski, 1972, Linear transformations which preserve trace and positive semidefiniteness of operators, Rep. Math. Phys. source
• Not checked yet

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

  cites [139] Zhao, 2014, Entangling different-color photons via time-resolved measurement and active feed forward, Phys. Rev. Lett. source
• Not checked yet

  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

In the paper

“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.”

In the paper

“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].”

What the sources say

• Not checked yet

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

  cites [123] Liu, 2013, Experimental measurement-device-independent quantum key distribution, Phys. Rev. Lett. source
• Not checked yet

  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
• Not checked yet

  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

In the paper

“In addition, it is also suggested that this challenges a fundamental principle of computer science, namely the extended Church-Turing thesis.”

What the sources say

• ?Not checked — no full text of the sourcecites [166] Żukowski, 1997, Realizable higher-dimensional two-particle entanglements via multiport beam splitters, Phys. Rev. A source
• ?Not checked — no full text of the sourcecites [167] Campos, 2000, Three-photon Hong–Ou–Mandel interference at a multiport mixer, Phys. Rev. A source

In the paper

“if more than two photons are interfered, a probability surface or coincidence landscape can be investigated [162]”

What the sources say

• Not checked yetcites [162] Zeilinger, 1993, Einstein–Podolsky–Rosen correlations in higher dimensions

In the paper

“and as such it is considered to be a promising candidate to show quantum supremacy.”

What the sources say

• ?Not checked — no full text of the sourcecites [166] Żukowski, 1997, Realizable higher-dimensional two-particle entanglements via multiport beam splitters, Phys. Rev. A source
• ?Not checked — no full text of the sourcecites [167] Campos, 2000, Three-photon Hong–Ou–Mandel interference at a multiport mixer, Phys. Rev. A source

In the paper

“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”

What the sources say

• Not checked yetcites [153] Okamoto, 2011, Realization of a Knill–Laflamme–Milburn controlled-not photonic quantum circuit combining effective optical nonlinearities, Proc. Natl Acad. Sci. source
• Not checked yetcites [154] Harrow, 2009, Quantum algorithm for linear systems of equations, Phys. Rev. Lett. source
• Not checked yetcites [155] Cai, 2013, Experimental quantum computing to solve systems of linear equations, Phys. Rev. Lett. source
• Not checked yet

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

  cites [156] Fisher, 2014, Quantum computing on encrypted data, Nat. Commun. source

In the paper

“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).”

In the paper

“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.”

What the sources say

• ?Not checked — no full text of the sourcecites [144] De Martini, 2002, Experimental realization of the quantum universal not gate, Nature source

In the paper

“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.”

In the paper

“two-photon interference enables the measurement of maximally entangled states through Bell states measurements, or equivalently, the projection onto the Bell basis.”

In the paper

“Two-photon interference is fundamentally interesting because it has no classical counterpart”

In the paper

“In quantum communication, it can be used to circumvent the problem of untrusted measurement devices, and build novel protocols.”

In the paper

“In quantum state analysis, it gives the possibility to distinguish between modes, since only indistinguishable states will bunch.”

In the paper

“with many applications ranging from precision measurement and state determination to quantum computations and quantum communication.”

In the paper

“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.”

In the paper

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

In the paper

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

In the paper

“Bell state measurements are central to the concepts of teleportation and entanglement swapping.”