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Cited by 16Quantum Information and CryptographyQuantum Mechanics and ApplicationsQuantum optics and atomic interactions

Nonlocal realism tests and quantum state tomography in Sagnac-based type-II polarization-entanglement SPDC-source

Open access
Motazedifard, Ali, Madani, S.A., Dashkasan, J.J., Vayaghan, N.S.·2021·Heliyon
DOI 10.1016/j.heliyon.2021.e07384PMC PMC8255184
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Abstract

. Furthermore, using the tomographic reconstruction of quantum states together a maximum-likelihood-technique (MLT) as the numerical optimization, we obtain the physical non-negative definite density operator which shows the nonseparability and entanglement of our prepared state. By having the maximum likelihood density operator, we calculate some important entanglement-measures and entanglement entropies. The Sagnac configuration provides bidirectional crystal pumping yields to high-rate entanglement source which is very applicable in quantum communication, sensing and metrology as well as quantum information protocols, and has potential to be used in quantum illumination-based LIDAR and free-space quantum key distribution (QKD).

AI snapshot

Written from the paper’s full text.

TL;DR

The paper reports an ultrabright, phase-stable type-II polarization-entangled SPDC source in a Sagnac interferometer using PPKTP, with strong violations of Bell/CHSH and Freedman inequalities and high fidelity to a Bell state. Quantum state tomography with maximum-likelihood reconstruction yields a physical density matrix and entanglement measures confirming nonseparability.

Key findings

  • The prepared state is close to the maximally entangled Bell state \(|\psi_{\text{Bell}}^{(-)}\rangle\) with fidelity \(F=97.8\pm0.1\%\).
  • Bell inequality measurement gives \(S=2.78\pm0.01\), violating the classical bound \(|S|\le2\); visibility is \(V_{HV}=99.969\pm0.008\%\) and \(V_{DA}=96.751\pm0.002\%\), both above the \(71\%\) classical threshold.
  • Freedman’s test gives positive parameters \(\delta_F^{(1)}=0.01715\pm0.00001\) and \(\delta_F^{(2)}=0.00375\pm0.00001\), violating the Freedman inequality.
  • Maximum-likelihood tomography yields eigenvalues \(p_\rho(j)=0.93368,0.06632,0,0\), \(\mathrm{tr}\hat{\rho}^2=0.875\), concurrence \(C=0.876\pm0.007\), tangle \(T=0.767\pm0.014\), entanglement of formation \(E=0.825\pm0.016\), Von Neumann entropy \(S=0.353\pm0.018\), linear entropy \(P=0.167\pm0.008\), Renyi 2-entropy \(\Upsilon_A=0.684\pm0.014\), and logarithmic negativity \(E_N(\rho)=0.898\pm0.008\).

Methods

  • Experimental setup: a 48 mW 405 nm diode laser was polarized at \(+45^\circ\) and used to bidirectionally pump a \(1\times2\times25\) mm PPKTP collinear crystal (\(\Lambda_0=10.025\ \mu\text{m}\)) inside a Sagnac interferometer at \(30^\circ\)C, generating type-II SPDC photon pairs at 810 nm; a QWP compensator was set at \(\phi\simeq35.5^\circ\), and HWP-plus-PBS boxes with filters, fibers, Excelitas SPCMs, and a quTools coincidence time-tagger (81 ps resolution, 5 ns coincidence window, 400 ms integration) were used for polarization analysis.
  • Nonlocality tests: visibility was measured in H/V and D/A bases; the CHSH Bell parameter \(S\) was obtained from 16 coincidence-count measurements; Freedman’s parameter \(\delta_F\) was obtained from coincidence measurements at \(\Phi=22.5^\circ\) and \(67.5^\circ\).
  • Quantum state tomography: 16 polarization-projection measurements using QWP/HWP/PBS combinations were combined with maximum-likelihood numerical optimization to reconstruct a nonnegative physical density operator; fidelity and entanglement entropies/measures were then calculated from the reconstructed matrix.

Limitations

  • The paper has no dedicated limitations section; it notes generally that SPDC’s probabilistic nature produces zero or multiple photon pairs with a Poissonian distribution, limiting applications such as complex algorithms requiring many qubits and gate operations.
  • Evident from the text: the reconstructed state is mixed rather than pure, as shown by Von Neumann entropy \(S=0.353\pm0.018\) and linear entropy \(P=0.167\pm0.008\), so it is close to but not exactly the maximally entangled Bell state.
  • Evident from the text: the reported uncertainty for \(V_{HV}\) differs between the abstract (\(\pm0.003\)) and the experimental results (\(\pm0.008\)), and no systematic-error budget or explicit discussion of experimental imperfections is provided.

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

Integrity signals

Registry

Crossref · 10.1016/j.heliyon.2021.e07384

Cites

70 of 70 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

8 of 24 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Using the theory of measurement of qubits, including tomographic reconstruction from 16 polarization measurements together with maximum-likelihood numerical optimization, one can obtain and reconstruct the non-negative definite density operator.

    “It has been shown theoretically and experimentally [56], [57], [58] that using the theory of the measurement of qubits, which includes a tomographic reconstruction of the DMOS due to the linear set of 16 polarization-measurements together with the numerical optimization method, the so-called maximum-likelihood-technique (MLT), one can obtain and reconstruct the non-negative definite density operat”
    Quote in the paperSubstantial claim3 of 3 sources checked
    • cites [56] James D.F.V. Kwiat P.G. Munro W.J. White A.G. Measurement of qubits Phys. Rev. A 64 2001 052312 also see site: http://research.physics.illinois.edu/QI/Photonics/Tomography/ source
    • cites [57] White A.G. James D.F.V. Eberhard Ph.H. Kwiat P.G. Nonmaximally entangled states: production, characterization, and utilization Phys. Rev. Lett. 83 1999 3103 source

      Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured
    • cites [58] Kwiat P.G. Waks E. White A.G. Appelbaum I. Eberhard Ph.H. Ultra-bright source of polarization-entangled photons Phys. Rev. A 60 1999 R773(R) source

      Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured
  • Findingown data

    By fitting the theoretical expression (7) to the experimental coincidence points, the average transmittance is ε̄fit = sqrt(εa εb) = 0.748 ± 0.015.

    “By fitting the theoretical expression (7) to the experimental coincidence pints, we obtain the average transmittance as ϵ¯fit=ϵaϵb=0.748±0.015.”
    Quote in the paperNot a substantial claim
  • Findingown data

    The measured Freedman parameter δF(2) is 0.00375 ± 0.00001 for a = 45° and b = 67.5° and 112.5°.

    “Our experimental data provide Freedman parameter with 5-digit accuracy as δF(1)=0.01715±0.00001 when a=0∘ and b=22.5∘ and 67.5∘; and δF(2)=0.00375±0.00001 when a=45∘ and b=67.5∘ and 112.5∘.”
    Quote in the paperSubstantial claim
  • Findingown data

    The measured visibility in the D/A basis is 96.751% with uncertainty ±0.002.

    “VDA=%(96.751±0.002)”
    • Also stated in: § Nonlocality tests · plain
      “we find VHV=%(99.969±0.008) and VDA=%(96.751±0.002) with 5-digit accuracy for the visibility in H/V and 45/135 (D/A) bases, respectively.”
    Quote in the paperSubstantial claim
  • Findingown data

    The measured Bell parameter is S = 2.78 ± 0.01.

    “We have obtained very reliable and very strong Bell violation as S=2.78±0.01 with high brightness VHV=%(99.969±0.003) and VDA=%(96.751±0.002) and very strong violation due to Freedman test as δF=0.01715±0.00001.”
    • Also stated in: § Nonlocality tests · boosted
      “The experimental measured rates for our prepared entangled state lead to Bell parameter S=2.78±0.01, which shows very reliable and strong violation.”
    Quote in the paperSubstantial claim
  • May combine two claims. 13
  • Classified as probably not a substantial claim. 6

  • May combine two claims.

    Premisecitation

    For any hidden-variable theories and arbitrary angles, the Bell parameter satisfies |S| ≤ 2, equivalent to a visibility of coincidence probability V ≤ 0.71 in both H-V and D-A bases.

    “It can be proved that for any HVTs and arbitrary angles, Bell parameter satisfies inequality |S|≤2 which is equivalent to the visibility of coincidence probability V≤0.71 in both H-V and D-A basis [54], [76], [77].”
    Quote in the paperSubstantial claim2 of 3 sources checked
    • cites [54] Dehlinger D. Mitchell M.W. Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory Am. J. Phys. 70 2002 903 source

      Section VIII (p. 6) states that the CHSH inequality holds for hidden-variable theories at arbitrary polarizer angles, and Section IX (p. 6) uses |S| > 2 as the violation threshold. The passages do not state that this is equivalent to a coincidence-probability visibility V ≤ 0.71 in both the H–V and D–A bases. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
    • cites [76] Clauser J.F. Horne M.A. Shimony A. Holt R.A. Proposed experiment to test local hidden-variable theories Phys. Rev. Lett. 23 1969 15,880 source

      The paper’s generalization of Bell’s theorem derives a bound for local hidden-variable theories, with locality and setting-independent hidden-variable distributions stated as assumptions (indexed Abstract section; page unavailable). Its discussion of inequality (2b) applies the bound to polarizer orientations, but the cited passages do not state a Bell parameter S or an equivalent coincidence-visibility limit of 0.71 in the H-V and D-A bases. The claim also overextends the result from local hidden-variable theories to any hidden-variable theory. (LLM, conf=0.90)

      Experimental — accuracy not yet measured
    • cites [77] Bell J.S. On the Einstein-Podolsky-Rosen paradox Physics (Long Island City, N.Y.) 1 1964 195 Wheeler J.A. Zurek W.H. Quantum Theory and Measurement 1983 Princeton U.P. Princeton, NJ source

  • May combine two claims.

    Premisecitation

    Freedman's inequality requires only 3 coincidence measurements and is simpler mathematically and experimentally than the standard CHSH Bell test.

    “Beyond the standard CHSH Bell test which requires 16 measurements, the so-called Freedman's inequality [79], [80] requires only 3 coincidence measurements with very simpler mathematical calculations and experiment, more understandable from the philosophical aspects and simpler physical interpretation, notably for undergraduate students in quantum optics Laboratories.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [79] Freedman S.J. Clauser J.F. Experimental test of local hidden-variable theories Phys. Rev. Lett. 28 1972 938 Freedman S.J. Experimental test of local hidden-variable theories Lawrence Berkeley Lab. Rep. 391 1972 source
    • cites [80] Brody J. Selton Ch. Quantum entanglement with Freedman's inequality Am. J. Phys. 86 2018 412 source

      In the section labeled “theories with high statistical accuracy” (page unavailable), inequality (3) uses coincidence rates at 22.5° and 67.5° normalized to a reference rate with both polarizers removed, supporting the three-rate description. The paper does not compare its measurement count, mathematical difficulty, or experimental simplicity with a 16-measurement CHSH test. (LLM, conf=0.82)

      Experimental — accuracy not yet measured

  • Classified as probably not a substantial claim.

    Premisecitation

    A type-II periodically poled PPKTP source has the potential to generate a type-II polarization-entangled Bell state.

    “This type of NLC has potential to generate the type-II polarization-entangled Bell-state (for more details about the state of SPDC, see Refs. [2], [12], [13]).”
    Quote in the paperSubstantial claim2 of 3 sources checked
    • cites [2] Shih Y. Entangled biphoton source-property and preparation Rep. Prog. Phys. 66 2003 1009 source
    • cites [12] Motazedifard A. Madani S.A. Vayaghan N.S. Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits arXiv:2012.02658v1 [quant-ph] 2020 source

      The Introduction and experimental-setup passages describe generating a polarization-entangled Bell state with paired type-I BBO crystals. Searches for PPKTP, periodically poled crystals, and type-II SPDC found no passage addressing whether a type-II PPKTP source can generate such a state. The different setup described in this paper does not contradict that possibility. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [13] Motazedifard A. Madani S.A. High-precision quantum transmittometry of DNA and methylene-blue using a frequency-entangled twin-photon beam in type-I SPDC OSA Contin. 4 3 2021 1049 source

      Section 2.3 (p. 4) says type-II SPDC generates photons with different polarizations, and Section 2.1 (p. 3) describes polarization-entangled Bell states and the wavepacket overlap needed to prepare them. The paper does not establish that a type-II PPKTP source can generate a Bell state; its experiment instead uses a type-I BBO crystal (Section 3.1, p. 7). (LLM, conf=0.84)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    The measured visibility in the H/V basis is 99.969%, reported with uncertainty ±0.008 in the Results/Table 1 and ±0.003 in the Abstract.

    “VHV=%(99.969±0.003)”
    • Also stated in: § Nonlocality tests · plain
      “we find VHV=%(99.969±0.008) and VDA=%(96.751±0.002) with 5-digit accuracy for the visibility in H/V and 45/135 (D/A) bases, respectively.”
    • Also stated in: § Nonlocality tests · plain
      “We obtain VHV=%(99.969±0.008) and VDA=%(96.751±0.002) for the visibility in H/V and 45/135 bases, respectively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The maximum-likelihood density operator reconstructed from the experimental tomographic data is the matrix in Eq. (13), with eigenvalues 0.93368, 0.06632, 0, 0 and trρ^2 = 0.875.

    “After numerical optimization using the measured tomographic data, the maximum-likelihood density operator matrix is obtained as(13)ρrec(MLT)=”
    • Also stated in: § Quantum state tomography · plain
      “with eigenvalues pρ(j)=0.93368,0.06632,0,0 (j=1,2,3,4) corresponding to trρˆ2=0.875.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The prepared type-II polarization-entangled state is high brightness, robust, and stable.

    “In this work, we experimentally prepared, measured and characterized high brightness, robust and stable type-II polarization-entangled state very close to the maximally entangled Bell-state with %98 fidelity via SPDC process in PPKTP NLC inside the SI.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    For Φab = 22.5° and 67.5°, the Freedman parameter becomes positive, showing a strong violation of Freedman's inequality.

    “As theory predicted for entangled state for Φab=22.5∘ and 67.5∘, Freedman parameter becomes positive which shows a strong violation.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    Quantum mechanics can violate the Bell inequality, and for maximally entangled Bell states the maximum S is S(QM) = 2√2 ≈ 2.81, while other quantum states give lower values.

    “Surprisingly, it can be proved that quantum mechanics can violate this inequality by considering entangled-state.”
    • Also stated in: § Nonlocality tests · plain
      “By choosing angles a=−45∘, b=−22.5∘, a′=0 (V), and b′=+22.5∘; we obtain [12], [77] S(QM)=22≃2.81 for any maximally entangled Bell-state, while other quantum states give lower values such that Smax=S(QM).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [12] Motazedifard A. Madani S.A. Vayaghan N.S. Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits arXiv:2012.02658v1 [quant-ph] 2020

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

    • cites [77] Bell J.S. On the Einstein-Podolsky-Rosen paradox Physics (Long Island City, N.Y.) 1 1964 195 Wheeler J.A. Zurek W.H. Quantum Theory and Measurement 1983 Princeton U.P. Princeton, NJ source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Bell showed that all hidden-variable theories obey his inequality, while quantum mechanics, for example an entangled state, violates it.

    “In 1964, Bell showed that all hidden-variable theories (HVTs) obey his inequality, while quantum mechanics, for example entangled state, violates [12], [77], [78].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [12] Motazedifard A. Madani S.A. Vayaghan N.S. Measurement of entropy and quantum coherence properties of two type-I entangled photonic qubits arXiv:2012.02658v1 [quant-ph] 2020

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

    • cites [77] Bell J.S. On the Einstein-Podolsky-Rosen paradox Physics (Long Island City, N.Y.) 1 1964 195 Wheeler J.A. Zurek W.H. Quantum Theory and Measurement 1983 Princeton U.P. Princeton, NJ source
    • cites [78] Aspect A. Grangier P. Experiments on Einstein–Podolsky–Rosentype correlations with pairs of visible photons Penrose R. Isham C.J. Quantum Concepts in Space and Time 1986 Oxford U.P. 1 44

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

  • May combine two claims.

    Premisecitation

    For any realistic and local theory, the Freedman parameter is always nonpositive, δF ≤ 0; if δF > 0, hidden-variable theories or classical physics cannot interpret it.

    “It can be proved that for any realistic and local theory such as classical physics, the Freedman parameter is always nonpositive, i.e., δF≤0. If in an experiment Freedman parameters reliably becomes positive, δF>0, thus, one says the HVTs or classical physics cannot interpret it.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    In the ideal case, for the Bell state (1), the coincidence rate can be theoretically calculated as Rc_theory = 1/2 sin2(α − β).

    “In the ideal case, for the Bell state (1), the coincidence rate can be theoretically calculates as Rctheory=12sin2⁡(α−β).”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisereasoning

    In experiment, if S > 2 (V > 0.71), it shows violation of the Bell inequality and indicates that nature does not agree with hidden-variable theories or classical physics.

    “In experiment, if S>2 (V>0.71), it shows the violation the Bell inequality and approves that the nature does not agree the HVTs or classical physics.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The measured Bell parameter S = 2.78 ± 0.01 shows a very reliable and strong violation of the Bell inequality/HVTs, with 78σstd.

    “The experimental measured rates for our prepared entangled state lead to Bell parameter S=2.78±0.01, which shows very reliable and strong violation.”
    • Also stated in: § Nonlocality tests · boosted
      “We have obtained S = 2.78 ± 0.01 which shows very reliable (with 78σstd) and strong violation from the HVTs or any classical prediction.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Sagnac-based sources, because of their stability and high rate, have been used in quantum optical experiments including quantum key distribution and nonclassical radiation sources.

    “Among the different configurations of interferometers, in recent decades, the Sagnac-based sources because of their stability and high rate have been used in quantum optical experiments in a variety range of application such as quantum key distribution (QKD) [43], [69] and nonclassical radiation sources [70], [71], [72], [73].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [43] Erven Ch. On Experimental Quantum Communication and Cryptography PhD thesis in Physics-Quantum Information 2012 University of Waterloo Canada

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

    • cites [69] Erven Ch. On Free Space Quantum Key Distribution and its Implementation with a Polarization-Entangled Parametric Down Conversion Source Master thesis in Physics 2007 University of Waterloo Canada

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

    • cites [70] Shi B. Tomita A. Generation of a pulsed polarization entangled photon pair using a Sagnac interferometer Phys. Rev. A 69 2004 013803 source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    If a density matrix is separable, all eigenvalues of its partial transpose are non-negative; if the eigenvalues are negative, the density matrix is entangled.

    “Therefore, if the density matrix ρˆ is separable, then, all eigenvalues of ρTA are non-negative. Otherwise, if the eigenvalues are negative; thus, ρˆ is entangled.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [82] Źyczkowski K. Horodecki P. Sanpera A. Lewenstein M. Volume of the set of separable states Phys. Rev. A 58 1998 883 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Logarithmic negativity is an upper bound to the distillable entanglement and is obtained from the Peres-Horodecki criterion for separability.

    “Finally, the Logarithmic negativity, as upper bound to the distillable entanglement, which is obtained from the Peres-Horodecki criterion for separability [82], is defined as(22)EN(ρ)=log2trρˆ†TAρˆTA,”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [82] Źyczkowski K. Horodecki P. Sanpera A. Lewenstein M. Volume of the set of separable states Phys. Rev. A 58 1998 883 source
16 of 16

  • The paper relies on this without support.

    The cleanest, easiest, most inexpensive, and most accessible entanglement source, notably polarization entanglement, can be realized via SPDC in bulk nonlinear crystals.

    “To our knowledge, the cleanest, easiest, and most inexpensive and accessible entanglement source, notably the polarization entanglement source, can be realized via the process of spontaneous parametric down-conversion (SPDC) in bulk nonlinear crystals (NLCs) such as BBO, PPKTP or BaBO.”

  • The paper relies on this without support.

    SPDC in bulk nonlinear crystals is more inexpensive, user-friendly, works at room temperature without cooling, and is scalable for commercialization.

    “One of the advantages of nonclassical sources based on the SPDC in bulk NLCs is that they are more inexpensive, user-friendly, and work at room-temperature, which means that need no cooling, and have capability to be scalable in order to be commercialized.”

  • The authors state this as an assumption.

    The eigenvalues ra(j) of the non-Hermitian matrix Rˆ are ordered such that r1≥r2≥r3≥r4.

    “with the left and right eigenstates, |ξL(R)(a)〉 and eigenvalues ra(j)=0.93,0.054,0,0 with assumption r1≥r2≥r3≥r4”
3 of 3

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.

  • H/V visibility is inconsistent with the measured coincidence rates

    Major

    The 0° measurements give a visibility of (14.7923−0.5376)/(14.7923+0.5376)=92.99%, not 99.969%. Combining both H/V measurement pairs gives approximately 94.54%.

  • Reported fidelity exceeds the reconstructed state's maximum possible fidelity

    Major

    The reported fidelity of 97.8% with a pure Bell state exceeds the reconstructed density operator's largest eigenvalue, 0.93368. A state's fidelity with any pure state cannot exceed its largest eigenvalue.

  • The 135° coincidence rates reverse the stated angular dependence

    Minor

    The paper's sin2 of the polarizer-angle difference predicts a minimum at 135°/135° and a maximum at 135°/45°. Table 1 instead reports 14.6600 Kcps and 0.2211 Kcps, respectively.

  • Abstract and results give different H/V visibility uncertainties

    Minor

    The abstract reports an uncertainty of ±0.003%, while the results report ±0.008% for the same H/V visibility.

  • Reported purity does not match the stated eigenvalues

    Minor

    Squaring and summing the stated eigenvalues gives trρˆ2=0.876155, which rounds to 0.876 rather than the reported 0.875.

5 of 5

Cites

Flagged first, then by citations

Research works printed but not linked: 2

  1. Motazedifard, 2014, Theoretical formulation and numerical simulation of 1D Fresnel diffraction from a phase step with two different kinds of material on sides of step in reflection mode, J. App. Phys. Univ. Alzahra, 2, 5
  2. Freedman, 1972, Experimental test of local hidden-variable theories, Lawrence Berkeley Lab. Rep., 391

Cited by

Sorted by citations

Authors
Motazedifard, A., Madani, S. A., Dashkasan, J. J., & Vayaghan, N. S.
Affiliations
Iranian Center for Quantum Technologies (IR)
Corresponding author
Motazedifard, Ali
ORCID
Motazedifard, Ali
Venue
Heliyon
Publisher
Elsevier BV
Published
2021-06
Volume
7
Issue
6
Pages
e07384
ISSN
2405-8440 (ISSN-L)
DOI
10.1016/j.heliyon.2021.e07384
PMC
PMC8255184
OpenAlex
W3110945407
Semantic Scholar
016dc5db7b79c472f1bdb617a70fa680e3cf353d
Cited by
16
References
66
Citations by year
2026: 4 · 2025: 4 · 2024: 3 · 2022: 3 · 2021: 2
FWCI
0.71
Type
journal article
Language
en
Open access
Licence
Locations
  • Heliyon (publishedVersion, cc-by-nc-nd)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • PubMed Central (submittedVersion, cc-by-nc-nd)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › 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
Sagnac interferometer, spontaneous parametric down-conversion, polarization entanglement, quantum state tomography, maximum likelihood estimation, entanglement measures, entanglement entropy, non-separability, quantum illumination, free-space quantum key distribution

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