Experimental hierarchy of two-qubit quantum correlations without state tomography
Open accessAbstract
A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.
AI snapshot
Written from the paper’s full text.
TL;DR
The paper reports an experimental demonstration of the hierarchy of two-qubit entanglement, steering, and Bell nonlocality for Werner states without full quantum state tomography, using only six elements of a correlation matrix \(R\). It also theoretically extends the hierarchy to generalized Werner states.
Key findings
- By measuring only six elements of \(R\) (linear combinations of two-qubit Stokes parameters) instead of 15 or 16 real parameters in full QST, the authors experimentally resolve the hierarchy for Werner states: separable, entangled but unsteerable and Bell local, steerable in the 3-measurement scenario but Bell local, and Bell nonlocal/steerable in the 2-measurement scenario.
- Experimental results (Tables 1 and 2; Figs. 3 and 4) agree with theory; for example, theory predicts FEF = 0.100 at \(p=0.4\) while \(B=S=0\), \(S=0.200\) at \(p=0.6\) while \(B=0\), and \(B=0.529\), \(S=0.678\), FEF = 0.700 at \(p=0.8\), with all measures equal to 1.000 at \(p=1.0\).
- The most entangled experimental Bell-like state had FEF = 0.9685 and purity of about 98.9%.
- The setup can also reveal the hierarchy for generalized Werner states—mixtures of an arbitrary two-qubit pure state and white noise—as analyzed theoretically via a hierarchy parameter defined in Eq. (33) and plotted in Fig. 1.
Methods
- Linear-optics platform with polarization-encoded qubits generated by spontaneous parametric down-conversion in a cascade of two Type-I BBO crystals in the Kwiat configuration, pumped by a frequency-doubled femtosecond laser at 413 nm.
- White noise was simulated by widening the coincidence window to aggregate random detections; Werner states were interpolated between two copies of the singlet Bell state and the maximally mixed state.
- The correlation matrix \(R\) was reconstructed from four-fold coincidence counts for local polarization projections; error bars were derived by a Monte Carlo method using a normal distribution of \(R\) components with variance corresponding to detected photocounts, and maximum-likelihood estimation was used.
Limitations
- The paper states that experimental imperfections, instability, Poisson randomness, and an imperfect Bell state reduce the measured correlation measures; 56.7% of photons do not interfere on the fiber beam splitter, the count rate is about one event per 5 minutes, and the most entangled Bell-like state has purity about 98.9%.
- The Costa–Angelo steering measures are invariant under qubit swapping, so they cannot reflect directional one-way steering; the LUR-based steering measure cannot be determined from \(R\) and was not calculated for this experimental data.
- The FEF is not a universal entanglement witness and depends only on \(R\); it is a good measure for generalized Werner states, while general entanglement measures also depend on single-qubit Stokes parameters. The experiment demonstrates the hierarchy for Werner states and theoretically for generalized Werner states, not for arbitrary two-qubit mixed states.
Model-written summary. Check it against the paper before relying on it.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
29 of 40 cited sources checked · 23 supported · 1 flagged · accuracy not yet measured
- Findingcitation
None of the experimental states of Ref.9 exhibited one-way steering.
“More importantly, none of those experimental states exhibited one-way steering.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
The steerable-weight discussion (p. 5) and Appendix B (p. 16) assess steering from Alice to Bob. I searched for one-way and asymmetric steering, including steering from Bob to Alice, but found no passage comparing both directions for the experimental states. Our copy therefore does not establish that none exhibited one-way steering. (LLM, conf=0.76)
Experimental — accuracy not yet measured
- Findingnone given
The experimental setup requires only a single Hong-Ou-Mandel interferometer instead of two, compared with the method of Ref.56.
“Namely from the experimental point of view, it only requires a single Hong–Ou–Mandel interferometer instead of two.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [56] Bovino, F. A. et al. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett. 95, 240407. https://doi.org/10.1103/physrevlett.95.240407 (2005). source
- Premisecitation
The design shares the same geometry with the entanglement-swapping protocol of Ref.48.
“Moreover, our design shares the same geometry with the entanglement-swapping protocol48.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [48] Bartkiewicz, K., Lemr, K., Černoch, A. & Miranowicz, A. Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography. Phys. Rev. A 95, 030102. https://doi.org/10.1103/physreva.95.030102 (2017). source
- Interpretationcitation
The experimental method of measuring the R matrix enables complete determination of steering measures, the fully entangled fraction, and Bell nonlocality measures.
“This experimental method of measuring the R matrix enables us a complete determination of not only steering measures, but also a fully entangled fraction (FEF)57 and Bell nonlocality measures58.”
Quote in the paperSubstantial claim1 of 2 sources checked- cites [57] Bennett, C. H., DiVincenzo, D. P., Smolin, J. A. & Wootters, W. K. Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824. https://doi.org/10.1103/physreva.54.3824 (1996). source
- cites [58] Horodecki, R., Horodecki, P. & Horodecki, M. Violating Bell inequality by mixed states: Necessary and sufficient condition. Phys. Lett. A 200, 340–344. https://doi.org/10.1016/0375-9601(95)00214-n (1995). source
- Premisecitation
S2=0 does not imply S1=0, as shown experimentally in Ref.9.
“Thus, (corresponding to vanishing Bell nonlocality of a given state ) does not imply that also , which was shown experimentally in Ref.9).”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
- Findingown data
The experimental setup can also reveal the hierarchy of these quantum correlations for generalized Werner states, which are any two-qubit pure states affected by white noise.
“We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.”
- Also stated in: § Introduction · plain
“Moreover, we show that the generalized Werner states (GWSs), which are mixtures of an arbitrary two-qubit pure state and white noise, can reveal a more refined hierarchy of the quantum-correlation measures using our experimental setup.”
Quote in the paperSubstantial claim - Also stated in: § Introduction · plain
- Findingown data
The paper experimentally demonstrated the hierarchy of measures of entanglement, steering, and Bell nonlocality for Werner states without full quantum state tomography, by measuring only six elements of a correlation matrix R (linear combinations of two-qubit Stokes parameters).
“Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters.”
- Also stated in: § Introduction · hedged
“Here, we report the first (to our knowledge) experimental demonstration of the hierarchy of measures of entanglement, steering, and Bell nonlocality without applying full QST, i.e., by measuring only six elements of a correlation matrix R (corresponding to linear combinations of two-qubit Stokes parameters) for the Werner states.”
Quote in the paperSubstantial claim- Rests on an assumption: No experiment has been performed to determine standard entanglement measures of a general two-qubit mixed state without full quantum state tomography.
- Also stated in: § Introduction · hedged
- Findingreasoning
With the matrix R, we were able to determine various measures of quantum entanglement, steerability, and Bell nonlocality of the Werner and Werner-like states.
“With the matrix R, we were able to determine various measures of quantum entanglement, steerability, and Bell nonlocality of the Werner and Werner-like states.”
Quote in the paperSubstantial claim - Findingown data
Both maximum likelihood estimation methods lead to R matrices that are essentially the same.
“Both methods lead to the R matrices that are essentially the same.”
Quote in the paperNot a substantial claim - Findingown data
Our experimental results demonstrate a very good agreement with our theoretical predictions.
“Our experimental results shown in Fig. 3 demonstrate a very good agreement with our theoretical predictions.”
Quote in the paperSubstantial claim - Findingown data
We have measured all the elements of the correlation matrix R for the Werner states with different amount of white noise.
“Specifically, we have measured all the elements of the correlation matrix R (which is symmetric by definition) for the Werner states with different amount of white noise.”
Quote in the paperSubstantial claim - Findingown data
56.7% of the photons do not interfere on FBS.
“We have performed a calibration measurement that reveals that 56.7% of the photons do not interfere on FBS.”
Quote in the paperSubstantial claim - Findingnone given
Our method relies on measuring only 6 real elements instead of 15 (or even 16) elements in a complete two-qubit QST.
“Specifically, our method relies on measuring only 6 real elements instead of 15 (or even 16) elements in a complete two-qubit QST.”
Quote in the paperSubstantial claim - Findingown data
The Costa-Angelo steering measures linearly depend on the mixing parameter p.
“It is clear that these measures linearly depend on the mixing parameter p.”
Quote in the paperNot a substantial claim - Findingown data
The experimentally generated singlet Bell state is not perfect.
“Also our experimentally generated singlet Bell state is not perfect.”
Quote in the paperNot a substantial claim - Findingnone given
There is a generation-time jitter that causes the visibility of two-photon interference on the FBS to decrease.
“Despite narrow frequency filtering on all photons (see the parameters of the bandpass filters in Fig. 2) and a relatively thin crystal cascade of twice 1 mm, there is a generation-time jitter, which causes the visibility of two-photon interference on the FBS to decrease.”
Quote in the paperSubstantial claim - Findingnone given
The nonzero regions of the correlation measures shown in both panels of Fig. 3 are the same.
“The nonzero regions of the correlation measures, shown in both panels of Fig. 3, are the same.”
Quote in the paperNot a substantial claim - Findingown data
Our experiment allows us to show the hierarchy of the tested quantum correlation measures.
“Most notably, our experiment allows us to show the hierarchy of the tested quantum correlation measures.”
Quote in the paperSubstantial claim - Interpretationreasoning
For generalized Werner states, the state is Bell nonlocal if and only if the mixing parameter p exceeds a threshold p_Bell(q) obtained by solving M=1 (Eq. 29).
“which means that is Bell nonlocal if .”
Quote in the paperSubstantial claim - Interpretationnone given
For generalized Werner states, the hierarchy inequalities of Eq. (30) reduce to Eq. (32).
“The inequalities in (30) for the GWSs reduce to32”
Quote in the paperNot a substantial claim - Interpretationreasoning
For generalized Werner states, the state is steerable in the three-measurement scenario if and only if the mixing parameter p exceeds a threshold p_unsteer(q) obtained by solving S3=0 (Eq. 18).
“which means that a given GWS, , is steerable assuming three measurements per qubit iff the mixing parameter .”
Quote in the paperSubstantial claim - Premisecitation
For standard Werner states, the state violates the CHSH inequality if and only if its mixing parameter p is greater than 1/√2.
“This function reduces for to the well-known result that the Werner state violates the CHSH inequality iff the mixing parameter 8.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [8] Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277. https://doi.org/10.1103/physreva.40.4277 (1989). source
- Interpretationcitation
For standard Werner states with mixing parameter p between 1/3 and 1/√2, the state is entangled although it does not violate the CHSH inequality.
“By comparing Eq. (26) with Eq. (8), it is clearly seen that the Werner states for the mixing parameter are entangled, although they do not violate the CHSH inequality, as was first predicted in Ref.8.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [8] Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277. https://doi.org/10.1103/physreva.40.4277 (1989). source
- Interpretationcitation
For generalized Werner states, the fully entangled fraction is exactly equal to the negativity and concurrence.
“In general, the FEF is only a witness of entanglement; however, for some special classes of two-qubit states, including the GWSs, the FEF becomes a good entanglement measure, and it reduces to the concurrence and negativity:6”
- Also stated in: § Fully entangled fraction and entanglement measures · plain
“It is seen that the negativity, concurrence, and FEF reduce to the same function for the GWSs.”
Quote in the paperNot a substantial claim - Also stated in: § Fully entangled fraction and entanglement measures · plain
- Interpretationreasoning
For standard Werner states, the state is unsteerable in the three-measurement scenario if and only if its mixing parameter is at or below the threshold given by Eq. (19).
“which imply that is unsteerable in the 3MS iff .”
Quote in the paperSubstantial claim - Interpretationreasoning
For generalized Werner states, the state is entangled if and only if the mixing parameter p exceeds a threshold p_sep(q) obtained by solving the separability condition (Eq. 7).
“This can be obtained by solving resulting in:7which means that is entangled iff .”
Quote in the paperNot a substantial claim - Interpretationcitation
The Bell nonlocality measures B and M are monotonically related to each other.
“Anyway, B and are monotonically related to each other:25”
Quote in the paperNot a substantial claim - Interpretationnone given
For a general two-qubit state, the discussed quantum correlation measures satisfy the hierarchy given by Eq. (30) (equivalently Eq. (31)).
“The following hierarchy of the discussed quantum correlation measures hold for a general two-qubit state :30or, equivalently,31”
Quote in the paperSubstantial claim - Interpretationreasoning
For ideal Werner states and generalized Werner states, any steering measures are symmetric (including LUR-based measures) for arbitrary p and q.
“Thus, any steering measures are symmetric (including those based on the LUR) for , , and with arbitrary p, q.”
Quote in the paperSubstantial claim - Premisenone given
The elements of R correspond to linear combinations of two-qubit Stokes parameters.
“These elements correspond to linear combinations of two-qubit Stokes parameters.”
Quote in the paperSubstantial claim - Interpretationnone given
Entanglement measures for general two-qubit states depend not only on the correlation matrix R but also on the single-qubit Stokes parameters.
“It should be noted that entanglement measures for general states, given in Eq. (1), depend not only on the correlation matrix R, but also on the single-qubit Stokes parameters for and .”
Quote in the paperSubstantial claim - Interpretationreasoning
By considerably widening the coincidence window by several orders of magnitude, the observed state becomes effectively white noise.
“By considerably widening that window by several orders of magnitude, we effectively aggregate also detections that are completely unrelated and mutually random. This way, the observed state becomes effectively white noise.”
Quote in the paperSubstantial claim - Interpretationown data
A specific threshold for steerability depends on the number of measurement settings, which in our case equal 2 and 3.
“It is clear that a specific threshold for steerability depends on the number of measurement settings which in our case equal 2 and 3.”
Quote in the paperSubstantial claim - Premisecitation
As shown in Ref.59, an arbitrary state described by a nondiagonal T can be transformed via singular-value decomposition into a state with a diagonal T by local unitary operations, without changing its quantum correlations.
“Anyway, as shown in Ref.59, an arbitrary state described by a nondiagonal T, can be transformed (via a singular-value decomposition) into a state with a diagonal T by local unitary operations, thus, without changing its quantum correlations, including those studied below.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites [59] Luo, S. Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303. https://doi.org/10.1103/PhysRevA.77.042303 (2008). source
- Interpretationreasoning
The purity of this Bell-like state is about 98.9%.
“This implies the purity of this Bell-like state of about 98.9%.”
Quote in the paperNot a substantial claim- The authors state this as an assumption: The rest of the measurement is nearly perfect when simulating imperfections by degrading the input Bell-like state.
- Premisenone given
The CHSH inequality is satisfied if and only if M ≤ 1.
“The CHSH inequality in (20) is satisfied iff .”
Quote in the paperNot a substantial claim - Premisecitation
Different thresholds have been found for different number of measurement settings.
“Different thresholds have been found for different number of measurement settings, see e.g. Refs.6,9,70.”
Quote in the paperSubstantial claim0 of 1 sources checked- cites Refs.6,9,70
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Interpretationnone given
The property that B equals the negativity, concurrence, steering measure S, and fully entangled fraction is not satisfied for M.
“This useful property of B is not satisfied for .”
Quote in the paperNot a substantial claim - Interpretationreasoning
The applied Costa-Angelo measures cannot reflect the directional property of EPR steering because they are invariant under qubit swapping.
“Finally, it is important to stress that the applied Costa–Angelo measures, because of their invariance under qubit swapping, cannot reflect the directional property of EPR steering that one qubit might be steerable by another, but not vice versa.”
Quote in the paperSubstantial claim - Interpretationreasoning
The fully entangled fraction is not a universal witness of two-qubit entanglement because it solely depends on the R matrix.
“It is seen that the FEF is not a universal witness of two-qubit entanglement, because it solely depends on the R matrix.”
Quote in the paperSubstantial claim - Interpretationreasoning
The prepared two copies of the Bell state are balanced enough to warrant the replacement of one operator by another.
“With respect to that we conclude that the prepared two copies of the Bell state are balanced enough to warrant the replacement of by .”
Quote in the paperSubstantial claim - Interpretationnone given
The Bell nonlocality measure B is exactly equal to the steering measure S2 in the two-measurement scenario.
“It is seen that is exactly equal to the steering measure , given in Eq. (13), in the 2MS.”
Quote in the paperNot a substantial claim - Interpretationreasoning
An extra measurement performed by Bob on his qubit, allowed in the scenario, can reveal the steerability of the state.
“This is possible because an extra measurement performed by Bob on his qubit, which is allowed in the scenario, can reveal the steerability of .”
Quote in the paperSubstantial claim - Interpretationnone given
In the experiment all imperfections of individual components decrease the resulting correlation measures.
“In the experiment all imperfections of individual components decrease the resulting correlation measures.”
Quote in the paperNot a substantial claim - Interpretationreasoning
The required types of measurements for reconstructing R and full QST are the same.
“But this is not the case, because the required types of measurements are the same in both reconstructions.”
Quote in the paperSubstantial claim
- May combine two claims. 15
- Classified as probably not a substantial claim. 18
- The quote only partly states this claim. 2
May combine two claims.
InterpretationreasoningThe steering measure S2 in the two-measurement scenario is equivalent to the Bell nonlocality measure B, but is fundamentally different from the steering measure S1 studied in Ref.9 because it corresponds to Alice (Bob) performing two (three) measurements.
“However, the steering measure , as defined in Eq. (13) in the 2MS, although it is equivalent to the Bell nonlocality measure B, but it is fundamentally different from another steering measure (for clarity denoted here as ) studied by us in Ref.9, because it corresponds to the case when Alice (Bob) performs two (three) measurements on her (his) qubit.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
Split into 2 atoms — 1 confirmed, 0 partially supported, 1 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measured
May combine two claims.
InterpretationcitationFor an arbitrary two-qubit pure state, the Bell nonlocality measure B is equal to the negativity and concurrence, and also to the steering measure S and the fully entangled fraction.
“On the other hand, B is equal to the negativity and concurrence37,66, but also to the steering measure S and the FEF:24for an arbitrary two-qubit pure state , where a, b, c, d are the normalized complex amplitudes.”
Quote in the paperSubstantial claim2 of 2 sources checked- cites [37] Miranowicz, A. & Grudka, A. A comparative study of relative entropy of entanglement, concurrence and negativity. J. Opt. B Quantum Semiclass Opt. 6, 542. https://doi.org/10.1088/1464-4266/6/12/009 (2004). source
- cites [66] Miranowicz, A. Violation of Bell inequality and entanglement of decaying Werner states. Phys. Lett. A 327, 272–283. https://doi.org/10.1016/j.physleta.2004.05.001 (2004). source
May combine two claims.
FindingcitationThe maximum steering difference for the experimental states of Ref.9 is practically negligible and much less than the corresponding error bars.
“Thus, the maximum steering difference for the experimental states of Ref.9 can be found to be , which is practically negligible and much less than the corresponding error bars.”
Quote in the paperSubstantial claim1 of 1 sources checked- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationSimilar quantifiers, but describing nonlocality and entanglement, were measured in Ref.48 using the parameters M and F, which are also applied in this paper.
“Similar quantifiers, but describing nonlocality and entanglement, were measured in Ref.48 using the parameters M and F, which are also applied in this paper.”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [48] Bartkiewicz, K., Lemr, K., Černoch, A. & Miranowicz, A. Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography. Phys. Rev. A 95, 030102. https://doi.org/10.1103/physreva.95.030102 (2017). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationA QST-based approach to study a hierarchy of quantum correlations was applied in the authors' former related study9, based on measuring 16 real parameters for two-qubit Werner states.
“Thus, a QST-based approach to study a hierarchy of quantum correlations was applied in our former related study9, which was based on measuring 16 real parameters for two-qubit Werner states.”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
Section II (p. 3) says the study used full quantum state tomography to investigate a hierarchy of correlations, and the experimental setup (pp. 7–8) includes Werner states. But the setup describes measurements under 36 two-photon projection combinations, not measurement of 16 real parameters; our copy does not substantiate that numerical detail. (LLM, conf=0.88)
Experimental — accuracy not yet measured
May combine two claims.
Premisenone givenAn experimental method for testing polarization entanglement without QST of general two-qubit states was proposed in Ref.42 based on measuring a collective universal witness of Ref.43, but has not been implemented experimentally yet.
“We note that an experimental method for testing polarization entanglement without QST of general two qubit states was proposed in Ref.42 based on measuring a collective universal witness of Ref.43. However, the method, to our knowledge, has not been implemented experimentally yet.”
Quote in the paperNot a substantial claim2 of 2 sources checked- cites [42] Bartkiewicz, K., Horodecki, P., Lemr, K., Miranowicz, A. & Życzkowski, K. Method for universal detection of two-photon polarization entanglement. Phys. Rev. A 91, 032315. https://doi.org/10.1103/PhysRevA.91.032315 (2015). source
- cites [43] Augusiak, R., Demianowicz, M. & Horodecki, P. Universal observable detecting all two-qubit entanglement and determinant-based separability tests. Phys. Rev. A 77, 030301. https://doi.org/10.1103/physreva.77.030301 (2008). source
May combine two claims.
PremisecitationThe setup enables entanglement swapping and measuring multicopy entanglement witnesses.
“Moreover, the setup enables entanglement swapping and measuring multicopy entanglement witnesses as inspired by Refs.55,56.”
Quote in the paperNot a substantial claim1 of 2 sources checked- cites [55] Horodecki, P. From limits of quantum operations to multicopy entanglement witnesses and state-spectrum estimation. Phys. Rev. A 68, 052101. https://doi.org/10.1103/PhysRevA.68.052101 (2003). source
- cites [56] Bovino, F. A. et al. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett. 95, 240407. https://doi.org/10.1103/physrevlett.95.240407 (2005). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe setup applied in this work was also used earlier in Refs.48-51 for conceptually different tasks.
“We note that the setup applied in this work was also used earlier in Refs.48–51, but for conceptually different tasks, e.g., measuring collective nonlinear witnesses of entanglement52,53, Bell nonlocality measure54, or diagnosing an entanglement-swapping protocol.”
Quote in the paperNot a substantial claim6 of 6 sources checked- cites [48] Bartkiewicz, K., Lemr, K., Černoch, A. & Miranowicz, A. Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography. Phys. Rev. A 95, 030102. https://doi.org/10.1103/physreva.95.030102 (2017). source
- cites [49] Lemr, K., Bartkiewicz, K. & Černoch, A. Experimental measurement of collective nonlinear entanglement witness for two qubits. Phys. Rev. A 94, 052334. https://doi.org/10.1103/PhysRevA.94.052334 (2016). source
- cites [50] Trávníček, V., Bartkiewicz, K., Černoch, A. & Lemr, K. Experimental diagnostics of entanglement swapping by a collective entanglement test. Phys. Rev. Appl. 14, 064071. https://doi.org/10.1103/PhysRevApplied.14.064071 (2020). source
- cites [51] Roik, J., Bartkiewicz, K., Černoch, A. & Lemr, K. Entanglement quantification from collective measurements processed by machine learning. Phys. Lett. A 446, 128270. https://doi.org/10.1016/j.physleta.2022.128270 (2022). source
- cites [52] Rudnicki, L., Horodecki, P. & Życzkowski, K. Collective uncertainty entanglement test. Phys. Rev. Lett. 107, 150502. https://doi.org/10.1103/PhysRevLett.107.150502 (2011). source
- cites [53] Rudnicki, L., Puchała, Z., Horodecki, P. & Życzkowski, K. Collectibility for mixed quantum states. Phys. Rev. A 86, 062329. https://doi.org/10.1103/PhysRevA.86.062329 (2012). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe experimental method of measuring R for general two-qubit states is conceptually similar to that reported in Ref.56 for measuring a nonlinear entropic witness.
“Our experimental method of measuring R for general two qubit states is conceptually similar to that reported in Ref.56 for measuring a nonlinear entropic witness.”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [56] Bovino, F. A. et al. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett. 95, 240407. https://doi.org/10.1103/physrevlett.95.240407 (2005). source
May combine two claims.
InterpretationcitationThe method can perform full tomography of all elements of the R matrix rather than only determining its trace, so from the six numbers one can learn much more about quantum correlations compared to the original method of Ref.56.
“As shown in Ref.48, one can perform a full tomography of all the elements of the R matrix rather than only determining its trace. Thus, from the set of six numbers (determining a correlation matrix R) we can learn much more about quantum correlations compared to the original method of Ref.56.”
Quote in the paperSubstantial claim2 of 2 sources checked- cites [48] Bartkiewicz, K., Lemr, K., Černoch, A. & Miranowicz, A. Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography. Phys. Rev. A 95, 030102. https://doi.org/10.1103/physreva.95.030102 (2017). source
- cites [56] Bovino, F. A. et al. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett. 95, 240407. https://doi.org/10.1103/physrevlett.95.240407 (2005). source
Our copy describes direct measurements of Rényi entropy and purity, and gives equations for traces of the bipartite state and its subsystems (Abstract; page unavailable). Searches for full tomography, an R matrix, and six numbers found no passage addressing whether the method determines every element of an R matrix. (LLM, conf=0.72)
Experimental — accuracy not yet measured
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe setup bears some similarities with a previously proposed and implemented scheme by Bovino et al.56.
“The setup also bears some similarities with a previously proposed and implemented scheme by Bovino et al.56.”
Quote in the paperNot a substantial claim1 of 1 sources checked- cites [56] Bovino, F. A. et al. Direct measurement of nonlinear properties of bipartite quantum states. Phys. Rev. Lett. 95, 240407. https://doi.org/10.1103/physrevlett.95.240407 (2005). source
Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationAnother experimental approach to determine entanglement without QST can be based on measuring a bipartite Schmidt number, which satisfies conditions of a good entanglement measure and can be determined experimentally via a witnessing approach.
“Another experimental approach to determine entanglement of a given state without QST can be based on measuring a bipartite Schmidt number, which satisfies various conditions of a good entanglement measure44,45 and can be determined experimentally via a witnessing approach46.”
Quote in the paperNot a substantial claim3 of 3 sources checked- cites [44] Terhal, B. M. & Horodecki, P. Schmidt number for density matrices. Phys. Rev. A 61, 040301. https://doi.org/10.1103/PhysRevA.61.040301 (2000). source
Split into 2 atoms — 1 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.
Experimental — accuracy not yet measured - cites [45] Sanpera, A., Bruß, D. & Lewenstein, M. Schmidt-number witnesses and bound entanglement. Phys. Rev. A 63, 050301. https://doi.org/10.1103/PhysRevA.63.050301 (2001). source
- cites [46] Sperling, J. & Vogel, W. Determination of the Schmidt number. Phys. Rev. A 83, 042315. https://doi.org/10.1103/PhysRevA.83.042315 (2011). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationExperimental QST-based hierarchies of quantum entanglement, steering, and Bell nonlocality for specific classes of two-qubit states were reported, including experiments with mixtures of partially entangled two-qubit pure states and GWSs based on full QST or full quantum process tomography.
“Experimental QST-based hierarchies of quantum entanglement, steering, and Bell nonlocality for specific classes of two-qubit states in relation to the above-mentioned estimations were also reported, which include experiments with mixtures of partially entangled two-qubit pure states41 and GWSs based on full QST9 or full quantum process tomography24.”
Quote in the paperNot a substantial claim2 of 3 sources checked- cites [41] Yang, H. et al. Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems. Opt. Express 29, 26822. https://doi.org/10.1364/oe.430964 (2021). source
- cites [9] Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K. & Miranowicz, A. Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise. Phys. Rev. A 104, 062436. https://doi.org/10.1103/physreva.104.062436 (2021). source
- cites [24] Ku, H.-Y. et al. Quantifying quantumness of channels without entanglement. PRX Quantum 3, 020338. https://doi.org/10.1103/PRXQuantum.3.020338 (2022). source
Section IV reports a photonic experiment demonstrating a hierarchy of breaking channels, and states that the qubit-depolarizing channel was characterized by full process tomography. Appendix E confirms that a process matrix was calculated from 36 measurements. The paper does not describe this as an experiment with generalized Werner states or as a QST-based hierarchy of entanglement, steering, and Bell nonlocality for two-qubit states. (LLM, conf=0.85)
Experimental — accuracy not yet measured
Probably not a substantial claim: may not pass S3 (load-bearing).
Findingown dataWe have also analyzed theoretically a hierarchy of some measures of quantum correlations for generalized Werner states, which are defined as arbitrary superpositions of a two-qubit partially-entangled pure state and white noise.
“We have also analyzed theoretically a hierarchy (shown in Fig. 1) of some measures of quantum correlations for generalized Werner states, which are defined as arbitrary superpositions of a two-qubit partially-entangled pure state and white noise.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
Findingnone givenThe laser power fluctuates over time yielding variable rates of photon-pairs generation.
“Moreover, the laser power fluctuates over time yielding variable rates of photon-pairs generation.”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningThe Costa-Angelo steering measures are invariant under qubit swapping and therefore describe only two-way-symmetric steering for arbitrary two-qubit states.
“This means that the steering measures are invariant under the qubit-swapping operation, and, thus, describe only two-way-symmetric steering for arbitrary two-qubit states.”
Quote in the paperSubstantial claimClassified as probably not a substantial claim.
InterpretationreasoningThe LUR-based steering measure cannot be determined from R because its definition requires knowledge of the correlation matrix T and the vectors and for a given density state.
“Note that cannot be determined from R, because its definition requires, in general, the knowledge of not only the correlation matrix T (or R), but also the vectors and for a given density state .”
Quote in the paperSubstantial claimMay combine two claims. The quote only partly states this claim.
InterpretationcitationFor generalized Werner states, the correlation matrix R is diagonal and given by Eq. (4).
“The correlation matrix R for the GWSs, given in Eq. (3), is diagonal and reads4”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningThe Bell nonlocality measure M depends linearly on the mixing parameter p of the Werner states and generalized Werner states, so its experimental estimation results in smaller error bars than B.
“In particular, as shown explicitly below, depends linearly on the mixing parameter p of the Werner states and GWSs, thus its experimental estimation results in smaller error bars compared to those of B.”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationFor standard Werner states, the state is separable if and only if its mixing parameter p is at most 1/3.
“which implies the well known fact8 that a given Werner state is separable iff its mixing parameter is .”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [8] Werner, R. F. Quantum states with Einstein–Podolsky–Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277. https://doi.org/10.1103/physreva.40.4277 (1989). source
Probably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe witness defined in the next section can be interpreted as the three-measurement steering measure S.
“We find that the witness, defined in the next section, can actually be interpreted as the three-measurement steering measure S.”
Quote in the paperNot a substantial claimProbably not a substantial claim: may not pass S3 (load-bearing).
InterpretationreasoningThe instability and natural Poisson randomness of measured coincidences result in measurement uncertainties.
“Together with the instability and a natural Poisson randomness of the measured coincidences, these effects result in measurement uncertainties.”
Quote in the paperNot a substantial claimMay combine two claims. The quote only partly states this claim.
InterpretationreasoningFor standard Werner states, the Bell nonlocality measures B and M are given by Eq. (26), which shows that the states are nonlocal if and only if p > 1/√2.
“The Bell nonlocality measures B and for the Werner states read26which explicitly shows that the states are nonlocal iff .”
Quote in the paperSubstantial claimProbably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.
PremisecitationThe authors of Ref.47 used a setup introducing losses and measured elements of a correlation matrix to determine the steering indicators.
“The authors used a setup introducing losses and measured elements of a correlation matrix to determine the steering indicators.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [47] Fan, X.-G. et al. Experimental detection of quantum steerability based on the critical radius in an all-optical system. Phys. Rev. A 107, 012419. https://doi.org/10.1103/PhysRevA.107.012419 (2023). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationA very recent Ref.47 showed experimentally that a critical steering radius is the most powerful among practical steering indicators.
“We note a very recent Ref.47, where it was shown experimentally that a critical steering radius is the most powerful among practical steering indicators.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [47] Fan, X.-G. et al. Experimental detection of quantum steerability based on the critical radius in an all-optical system. Phys. Rev. A 107, 012419. https://doi.org/10.1103/PhysRevA.107.012419 (2023). source
Probably not a substantial claim: may not pass S3 (load-bearing).
PremisecitationThe scaling property of the critical steering radius allows classifying various families of quantum states as steerable or non-steerable.
“Its scaling property allows classifying as steerable or non-steerable various families of quantum states.”
Quote in the paperNot a substantial claim0 of 1 sources checked- cites [47] Fan, X.-G. et al. Experimental detection of quantum steerability based on the critical radius in an all-optical system. Phys. Rev. A 107, 012419. https://doi.org/10.1103/PhysRevA.107.012419 (2023). source
Probably not a substantial claim: may not pass S4 (based).
Interpretationnone givenThe use of measures or universal witnesses is required to demonstrate experimentally such hierarchies in a sufficient and necessary manner.
“The use of measures or universal witnesses of these quantum correlations, however, is required to demonstrate experimentally such hierarchies in a sufficient and necessary manner.”
Quote in the paperNot a substantial claimClassified as probably not a substantial claim.
Interpretationnone givenIt is not clear how the Schmidt-number method can also be used to experimentally determine steering and nonlocality measures.
“However, it is not clear how the same method can also be used to experimentally determine steering and nonlocality measures.”
Quote in the paperSubstantial claimMay combine two claims.
Interpretationown dataThe correlation matrices T and R are in general nondiagonal, although they are diagonal for the perfect generalized Werner states.
“We note that the correlation matrices T and R are in general nondiagonal (including the non-perfect Werner state measured by us experimentally), although they are diagonal for the perfect GWSs states given in Eq. (3).”
Quote in the paperNot a substantial claimMay combine two claims.
InterpretationreasoningFor generalized Werner states, the Bell nonlocality measures B and M are given by Eq. (27) and Eq. (28).
“For the GWSs, formulas in Eq. (26) generalize to:2728”
Quote in the paperSubstantial claimMay combine two claims.
InterpretationreasoningThe measures of steering S in the 3MS and of Bell nonlocality (B) are much steeper functions and are much more sensitive to unavoidable fluctuations of measured coincidence counts.
“By contrast to those quantifiers, the measures of steering S in the 3MS and of Bell nonlocality (B) are much steeper functions and that is why they are much more sensitive to unavoidable fluctuations of measured coincidence counts, as reflected in all the derived quantities.”
Quote in the paperSubstantial claim
The paper relies on this without support.
No experiment has been performed to determine standard entanglement measures of a general two-qubit mixed state without full quantum state tomography.
“For example, to our knowledge, no experiment has been performed to determine standard entanglement measures of a general two-qubit mixed state without full quantum state tomography (QST).”
The authors state this as an assumption.
The LUR-based steering measure for the experimental data reported here would be negligible, as it was for the experimental states reported in Ref.9.
“As explained above, cannot be calculated, in general, from R, so one cannot calculate for the experimental data reported here, but one can reasonably assume that would be negligible as those for the experimental states reported in Ref.9.”
The paper relies on this without support.
Modifications of the Werner states or generalized Werner states (such as replacing the singlet state by another pure state or using isotropic states) do not affect their quantum correlation measures.
“Such modifications of the Werner states or the GWSs do not affect their quantum correlation measures.”
The paper relies on this without support.
When two polarization states of single photons interact on a beam splitter and one of them is a maximally mixed state, the resulting probability of coincidence detection is independent of the state of the other photon.
“In order to do so, we make use of the fact that when two polarization states of single photons interact on a beam splitter and one of them is being a maximally mixed state, the resulting probability of coincidence detection is independent of the state of the other photon.”
The authors state this as an assumption.
The rest of the measurement is nearly perfect when simulating imperfections by degrading the input Bell-like state.
“We tried to simulate all these mentioned imperfections by degrading the input Bell-like state assuming the rest of the measurement to be nearly perfect.”
Cites
Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.865 · Cited by 10,118 · see citing works
Proposed Experiment to Test Local Hidden-Variable Theories
Clauser, J. F., Horne, M. A., Shimony, A., & Holt, R. A. (1969) · Physical Review Letters · doi:10.1103/physrevlett.23.880 · Cited by 7,573 · cited 1× · see citing works
“The Bell nonlocality of a given two-qubit state ρ can be tested by the violation of the Bell inequality in the Clauser-Horne-Shimony-Holt (CHSH) form [61] |〈B〉ρ| ≡ ∣∣〈a·σ⊗(b+b′)·σ+a′·σ⊗(b−b′)·σ〉 ρ ∣∣ ≤ 2, (20)”
Mixed-state entanglement and quantum error correction
Bennett, C. H., DiVincenzo, D. P., Smolin, J. A., & Wootters, W. K. (1996) · Physical Review A · doi:10.1103/physreva.54.3824 · Cited by 5,272 · cited 2× · see citing works
“The FEF [56] for an arbitrary two-qubit state ρ in Eq.”
BackgroundMethodQuantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · cited 3× · see citing works
“This function implies for q = 1/2 the wellknown result that the Werner state violates the CHSH inequality iff the mixing parameter p ∈ (1/ √ 2, 1] [8].”
BackgroundInfluentialNew High-Intensity Source of Polarization-Entangled Photon Pairs
Kwiat, P. G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A. V., & Shih, Y. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4337 · Cited by 3,102 · see citing works
Entanglement of a pair of quantum bits
Hill, S., & Wootters, W. K. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.5022 · Cited by 2,823 · cited 2× · see citing works
“These measures include the concurrence [27], which is a measure of the entanglement of formation, the negativity [28] quantifying the Peres-Horodecki entanglement criterion, and the relative entropy of entanglement [29].”
BackgroundMethodBrunner, N., Cavalcanti, D., Pironio, S., Scarani, V., & Wehner, S. (2014) · Reviews of Modern Physics · doi:10.1103/revmodphys.86.419 · Cited by 2,688 · cited 2× · see citing works
“Note that semidefinite programming has been found very effective in calculating not only nonuniversal witnesses but also measures (or universal witnesses) of quantum steering [3, 21, 22], Bell nonlocality [5], and entanglement [2].”
BackgroundSteering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox
Wiseman, H. M., Jones, S. J., & Doherty, A. C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.140402 · Cited by 1,553 · see citing works
Entanglement measures and purification procedures
Vedral, V., & Plenio, M. B. (1998) · Physical Review A · doi:10.1103/physreva.57.1619 · Cited by 1,419 · cited 1× · see citing works
“These measures include the concurrence [27], which is a measure of the entanglement of formation, the negativity [28] quantifying the Peres-Horodecki entanglement criterion, and the relative entropy of entanglement [29].”
BackgroundVolume of the set of separable states
Życzkowski, K., Horodecki, P., Sanpera, A., & Lewenstein, M. (1998) · Physical Review A · doi:10.1103/physreva.58.883 · Cited by 1,411 · cited 2× · see citing works
“Moreover, we recall the definition of the negativity N of a two-qubit state ρ, which reads [28]: N(ρ) = θ(−2μmin) with μmin denoting the smallest eigenvalue of ρ, i.”
BackgroundQuantum discord for two-qubit systems
Luo, S. (2008) · Physical Review A · doi:10.1103/physreva.77.042303 · Cited by 1,060 · cited 1× · see citing works
“[58], an arbitrary state ρ described by a nondiagonal T , can be transformed (via a singular-value decomposition) into a state with a diagonal T by local unitary operations, thus, without changing its quantum correlations, including those studied below.”
BackgroundViolating Bell inequality by mixed states: necessary and sufficient condition
Horodecki, R., Horodecki, P., & Horodecki, M. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00214-n · Cited by 884 · cited 2× · see citing works
“This experimental method of measuring the R matrix enables us a complete determination of not only steering measures, but also a fully entangled fraction (FEF) [56] and Bell nonlocality measures [57].”
MethodA convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
Navascués, M., Pironio, S., & Acín, A. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/7/073013 · Cited by 702 · see citing works
Uola, R., Costa, A. C. S., Nguyen, H. C., & Gühne, O. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015001 · Cited by 607 · cited 1× · see citing works
“Among different types of correlations, a special interest has been paid to quantum entanglement [2], EinsteinPodolsky-Rosen (EPR) steering (also called quantum steering) [3, 4], and Bell nonlocality that can be revealed by testing the violation of a Bell inequality [5].”
BackgroundExperimental criteria for steering and the Einstein-Podolsky-Rosen paradox
Cavalcanti, E. G., Jones, S. J., Wiseman, H. M., & Reid, M. D. (2009) · Physical Review A · doi:10.1103/physreva.80.032112 · Cited by 604 · cited 1× · see citing works
“The quantum steerability of a given two-qubit state ρ can be experimentally tested, assuming that each party is allowed to measure n observables in their sites (qubit), by the inequality derived by Cavalcanti, Jones, Wiseman, and Reid (CJWR), which reads [59]:”
MethodBounding the Set of Quantum Correlations
Navascués, M., Pironio, S., & Acín, A. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.010401 · Cited by 536 · cited 1× · see citing works
“which enabled finding a hierarchy of upper bounds on Bell nonlocality [16, 17] (iv) a hierarchy of EPR steering witnesses [18] based on entanglement criteria with the constraint that measurement devices of one party cannot be trusted.”
BackgroundEntanglement, Einstein-Podolsky-Rosen correlations, Bell nonlocality, and steering
Jones, S. J., Wiseman, H. M., & Doherty, A. C. (2007) · Physical Review A · doi:10.1103/physreva.76.052116 · Cited by 511 · see citing works
Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering
Piani, M., & Watrous, J. (2015) · Physical Review Letters · doi:10.1103/physrevlett.114.060404 · Cited by 467 · cited 2× · see citing works
“Note that semidefinite programming has been found very effective in calculating not only nonuniversal witnesses but also measures (or universal witnesses) of quantum steering [3, 21, 22], Bell nonlocality [5], and entanglement [2].”
BackgroundQuantum steering: a review with focus on semidefinite programming
Cavalcanti, D., & Skrzypczyk, P. (2016) · Reports on Progress in Physics · doi:10.1088/1361-6633/80/2/024001 · Cited by 454 · cited 1× · see citing works
“(3), change under qubit swapping, but still can be transformed into a swapping-invariant ρ′ GW(p, q) by local unitary operations.”
BackgroundExperimental EPR-steering using Bell-local states
Saunders, D. J., Jones, S. J., Wiseman, H. M., & Pryde, G. J. (2010) · Nature Physics · doi:10.1038/nphys1766 · Cited by 439 · see citing works
Schmidt number for density matrices
Terhal, B. M., & Horodecki, P. (2000) · Physical Review A · doi:10.1103/physreva.61.040301 · Cited by 427 · cited 1× · see citing works
“Another experimental approach to determine entanglement of a given state without QST can be based on measuring a bipartite Schmidt number, which satisfies various conditions of a good entanglement measure [43, 44] and can be determined experimentally via a witnessing approach [45].”
BackgroundComplete family of separability criteria
Doherty, A. C., Parrilo, P. A., & Spedalieri, F. M. (2004) · Physical Review A · doi:10.1103/physreva.69.022308 · Cited by 418 · see citing works
Observation of one-way Einstein–Podolsky–Rosen steering
Händchen, V., Eberle, T., Steinlechner, S., Samblowski, A., Franz, T., Werner, R. F., & Schnabel, R. (2012) · Nature Photonics · doi:10.1038/nphoton.2012.202 · Cited by 379 · see citing works
Quantifying Einstein-Podolsky-Rosen Steering
Skrzypczyk, P., Navascués, M., & Cavalcanti, D. (2014) · Physical Review Letters · doi:10.1103/physrevlett.112.180404 · Cited by 363 · cited 2× · see citing works
“Note that semidefinite programming has been found very effective in calculating not only nonuniversal witnesses but also measures (or universal witnesses) of quantum steering [3, 21, 22], Bell nonlocality [5], and entanglement [2].”
BackgroundInseparability Criteria for Continuous Bipartite Quantum States
Shchukin, E. V., & Vogel, W. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.230502 · Cited by 353 · cited 1× · see citing works
“For example: (i) hierarchies of various witnesses of spatial [10] and spatiotemporal [11, 12] correlations of bosonic systems revealing their nonclassicality via a nonpositive Glauber-Sudarshan P function; (ii) a hierarchy of entanglement witnesses [13, 14] based on the Peres-Horodecki partial transposition criterion…”
MethodSchmidt-number witnesses and bound entanglement
Sanpera, A., Bruß, D., & Lewenstein, M. (2001) · Physical Review A · doi:10.1103/physreva.63.050301 · Cited by 233 · cited 1× · see citing works
“Another experimental approach to determine entanglement of a given state without QST can be based on measuring a bipartite Schmidt number, which satisfies various conditions of a good entanglement measure [43, 44] and can be determined experimentally via a witnessing approach [45].”
BackgroundEntanglement versus Bell Violations and Their Behavior under Local Filtering Operations
Verstraete, F., & Wolf, M. M. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.170401 · Cited by 205 · cited 2× · see citing works
“The inequalities in (30) for the GWSs reduce to”
BackgroundNonclassicality of Quantum States: A Hierarchy of Observable Conditions
Richter, T., & Vogel, W. (2002) · Physical Review Letters · doi:10.1103/physrevlett.89.283601 · Cited by 192 · cited 1× · see citing works
“For example: (i) hierarchies of various witnesses of spatial [10] and spatiotemporal [11, 12] correlations of bosonic systems revealing their nonclassicality via a nonpositive Glauber-Sudarshan P function; (ii) a hierarchy of entanglement witnesses [13, 14] based on the Peres-Horodecki partial transposition criterion…”
MethodQuantification of Einstein-Podolski-Rosen steering for two-qubit states
Costa, A. C. S., & Angelo, R. M. (2016) · Physical Review A · doi:10.1103/physreva.93.020103 · Cited by 185 · cited 8× · see citing works
“The steering measures given in (11) can be rewritten in terms of the correlation matrix R as follows: S3(ρ) = θ( √ TrR− 1)√ 3− 1 , (12) S2(ρ) = θ {√ TrR−min[eig(R)]− 1 } √ 2− 1 , (13) The Costa-Angelo measure S3 of steering in the 3MS is sometimes modified as (see, e.g., Refs.”
BackgroundMethodInfluentialTesting nonclassicality in multimode fields: A unified derivation of classical inequalities
Miranowicz, A., Bartkowiak, M., Wang, X., Liu, Y.-X., & Nori, F. (2010) · Physical Review A · doi:10.1103/physreva.82.013824 · Cited by 184 · see citing works
Self-citationDirect Measurement of Nonlinear Properties of Bipartite Quantum States
Bovino, F. A., Castagnoli, G., Ekert, A., Horodecki, P., Alves, C. M., & Sergienko, A. V. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.240407 · Cited by 168 · cited 1× · see citing works
“[55] for measuring a nonlinear entropic witness.”
Quantum Computing: An Applied Approach
Hidary, J. D. (2019) · Springer eBooks · doi:10.1007/978-3-030-23922-0 · Cited by 149 · see citing works
Hierarchy of Steering Criteria Based on Moments for All Bipartite Quantum Systems
Kogias, I., Skrzypczyk, P., Cavalcanti, D., Acín, A., & Adesso, G. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.210401 · Cited by 123 · cited 1× · see citing works
“which enabled finding a hierarchy of upper bounds on Bell nonlocality [16, 17] (iv) a hierarchy of EPR steering witnesses [18] based on entanglement criteria with the constraint that measurement devices of one party cannot be trusted.”
BackgroundQuantifying Non-Markovianity with Temporal Steering
Chen, S.-L., Lambert, N., Li, C., Miranowicz, A., Chen, Y.-N., & Nori, F. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.020503 · Cited by 108 · cited 1× · see citing works
“[24], where the effects of white noise (or, equivalently, a qubit-depolarizing channel) on quantum memory, temporal steerability [25, 26], and nonmacrorealism were revealed by applying a full quantum process tomography.”
MethodSelf-citationComplete hierarchies of efficient approximations to problems in entanglement theory
Eisert, J., Hyllus, P., Gühne, O., & Curty, M. (2004) · Physical Review A · doi:10.1103/physreva.70.062317 · Cited by 101 · cited 2× · see citing works
“The CHSH inequality in (20) is satisfied iff M(σ ) ≤ 1 .”
BackgroundFrom limits of quantum operations to multicopy entanglement witnesses and state-spectrum estimation
Horodecki, P. (2003) · Physical Review A · doi:10.1103/physreva.68.052101 · Cited by 98 · see citing works
Ordering two-qubit states with concurrence and negativity
Miranowicz, A., & Grudka, A. (2004) · Physical Review A · doi:10.1103/physreva.70.032326 · Cited by 98 · cited 2× · see citing works
“Note that such estimations can also be applied to compare nonequivalent measures describing the same type of correlations, including two-qubit entanglement [36] or singlequbit nonclassicality [37].”
BackgroundSelf-citation3 Maximum-Likelihood Methodsin Quantum Mechanics
Hradil, Z., Řeháček, J., Fiurášek, J., & Ježek, M. (2004) · Lecture notes in physics · doi:10.1007/978-3-540-44481-7_3 · Cited by 95 · see citing works
Entanglement estimation from Bell inequality violation
Bartkiewicz, K., Horst, B., Lemr, K., & Miranowicz, A. (2013) · Physical Review A · doi:10.1103/physreva.88.052105 · Cited by 94 · cited 1× · see citing works
“(31) S2(ρ) ≤ S3(ρ) ≤ FEF(ρ) ≤ N(ρ) ≤ C(ρ),”
Self-citationNonclassical Correlation Properties of Radiation Fields
Vogel, W. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.013605 · Cited by 91 · cited 1× · see citing works
“For example: (i) hierarchies of various witnesses of spatial [10] and spatiotemporal [11, 12] correlations of bosonic systems revealing their nonclassicality via a nonpositive Glauber-Sudarshan P function; (ii) a hierarchy of entanglement witnesses [13, 14] based on the Peres-Horodecki partial transposition criterion…”
MethodNambu, Y., Usami, K., Tsuda, Y., Matsumoto, K., & Nakamura, K. T. (2002) · Physical Review A · doi:10.1103/physreva.66.033816 · Cited by 91 · cited 1× · see citing works
“To achieve a high degree of entanglement, the pumping pulse is diagonally polarized (by the half-wave plate HWPA) and subject to a polarization dispersion line [64].”
BackgroundUniversal observable detecting all two-qubit entanglement and determinant-based separability tests
Augusiak, R., Demianowicz, M., & Horodecki, P. (2008) · Physical Review A · doi:10.1103/physreva.77.030301 · Cited by 89 · see citing works
Entangling the Spatial Properties of Laser Beams
Wagner, K., Janoušek, J., Delaubert, V., et al. (2008) · Science · doi:10.1126/science.1159663 · Cited by 87 · see citing works
A comparative study of relative entropy of entanglement, concurrence and negativity
Miranowicz, A., & Grudka, A. (2004) · Journal of Optics B: Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/12/009 · Cited by 86 · see citing works
Self-citationHorst, B., Bartkiewicz, K., & Miranowicz, A. (2013) · Physical Review A · doi:10.1103/physreva.87.042108 · Cited by 80 · cited 1× · see citing works
“(32) B(ρGW) ≤ S(ρGW) ≤ FEF(ρGW) = N(ρGW) = C(ρGW).”
Self-citationInseparability criteria based on matrices of moments
Miranowicz, A., Piani, M., Horodecki, P., et al. (2009) · Physical Review A · doi:10.1103/physreva.80.052303 · Cited by 79 · cited 1× · see citing works
“For example: (i) hierarchies of various witnesses of spatial [10] and spatiotemporal [11, 12] correlations of bosonic systems revealing their nonclassicality via a nonpositive Glauber-Sudarshan P function; (ii) a hierarchy of entanglement witnesses [13, 14] based on the Peres-Horodecki partial transposition criterion…”
MethodSelf-citationSun, W., Wang, D., Shi, J., & Ye, L. (2017) · Scientific Reports · doi:10.1038/srep39651 · Cited by 73 · see citing works
Miranowicz, A., Bartkiewicz, K., Pathak, A., Peřina, J., Chen, Y.-N., & Nori, F. (2015) · Physical Review A · doi:10.1103/physreva.91.042309 · Cited by 68 · see citing works
Self-citationViolation of Bell inequality and entanglement of decaying Werner states
Miranowicz, A. (2004) · Physics Letters A · doi:10.1016/j.physleta.2004.05.001 · Cited by 68 · cited 1× · see citing works
“On the other hand, B is equal to the negativity and concurrence [36, 62], but also to the steering measure S and the FEF:”
BackgroundSelf-citationCertifying Einstein-Podolsky-Rosen steering via the local uncertainty principle
Zhen, Y.-Z., Zheng, Y.-L., Cao, W.-F., Li, L., Chen, Z., Liu, N.-L., & Chen, K. (2016) · Physical Review A · doi:10.1103/physreva.93.012108 · Cited by 64 · see citing works
Comment on “Inseparability Criteria for Continuous Bipartite Quantum States”
Miranowicz, A., & Piani, M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.058901 · Cited by 55 · cited 1× · see citing works
“For example: (i) hierarchies of various witnesses of spatial [10] and spatiotemporal [11, 12] correlations of bosonic systems revealing their nonclassicality via a nonpositive Glauber-Sudarshan P function; (ii) a hierarchy of entanglement witnesses [13, 14] based on the Peres-Horodecki partial transposition criterion…”
MethodSelf-citationDetermination of the Schmidt number
Sperling, J., & Vogel, W. (2011) · Physical Review A · doi:10.1103/physreva.83.042315 · Cited by 47 · cited 1× · see citing works
“Another experimental approach to determine entanglement of a given state without QST can be based on measuring a bipartite Schmidt number, which satisfies various conditions of a good entanglement measure [43, 44] and can be determined experimentally via a witnessing approach [45].”
BackgroundHierarchy of quantum correlations using a linear beam splitter
Qureshi, H. S., Ullah, S., & Ghafoor, F. (2018) · Scientific Reports · doi:10.1038/s41598-018-34463-y · Cited by 44 · cited 1× · see citing works
“, theoretical analyses of two-qubit Xstates [38] and two-mode Gaussian states [39].”
BackgroundQuantifying Quantumness of Channels Without Entanglement
Ku, H.-Y., Kadlec, J., Černoch, A., Quintino, M. T., Zhou, W., Lemr, K., Lambert, N., Miranowicz, A., Chen, S.-L., Nori, F., et al. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.020338 · Cited by 42 · cited 2× · see citing works
“[24], where the effects of white noise (or, equivalently, a qubit-depolarizing channel) on quantum memory, temporal steerability [25, 26], and nonmacrorealism were revealed by applying a full quantum process tomography.”
MethodSelf-citationBartkiewicz, K., Lemr, K., Černoch, A., & Miranowicz, A. (2017) · Physical Review A · doi:10.1103/physreva.95.030102 · Cited by 39 · see citing works
Self-citationMethod for universal detection of two-photon polarization entanglement
Bartkiewicz, K., Horodecki, P., Lemr, K., Miranowicz, A., & Życzkowski, K. (2015) · Physical Review A · doi:10.1103/physreva.91.032315 · Cited by 36 · cited 1× · see citing works
“[41] based on measuring a collective universal witness of Ref.”
Self-citationHierarchy in temporal quantum correlations
Ku, H.-Y., Chen, S.-L., Lambert, N., et al. (2018) · Physical Review A · doi:10.1103/physreva.98.022104 · Cited by 35 · cited 1× · see citing works
“It could also be noted that a hierarchy of quantum nonbreaking channels, which is closely related to a hierarchy of temporal [23] and spatial quantum correlations, has been studied very recently both theoretically and experimentally in Ref.”
BackgroundSpatio-Temporal Steering for Testing Nonclassical Correlations in Quantum Networks
Chen, S.-L., Lambert, N., Li, C.-M., Chen, G.-Y., Chen, Y.-N., Miranowicz, A., & Nori, F. (2017) · Scientific Reports · doi:10.1038/s41598-017-03789-4 · Cited by 34 · see citing works
Self-citationCollective Uncertainty Entanglement Test
Rudnicki, Ł., Horodecki, P., & Życzkowski, K. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.150502 · Cited by 31 · cited 1× · see citing works
“, measuring collective nonlinear witnesses of entanglement [51, 52], Bell nonlocality measure [53], or diagnosing an entanglement-swapping protocol.”
BackgroundEntanglement quantification from collective measurements processed by machine learning
Roik, J., Bartkiewicz, K., Černoch, A., & Lemr, K. (2022) · Physics Letters A · doi:10.1016/j.physleta.2022.128270 · Cited by 26 · see citing works
Self-citationJiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K., & Miranowicz, A. (2021) · Physical Review A · doi:10.1103/physreva.104.062436 · Cited by 24 · cited 20× · see citing works
“[9], because it corresponds to the case when Alice (Bob) performs two (three) measurements on her (his) qubit.”
BackgroundMethodResultInfluentialSelf-citationEntanglement as upper bound for the nonlocality of a general two-qubit system
Su, Z., Tan, H., & Li, X. (2020) · Physical Review A · doi:10.1103/physreva.101.042112 · Cited by 21 · see citing works
Collectibility for mixed quantum states
Rudnicki, Ł., Puchała, Z., Horodecki, P., & Życzkowski, K. (2012) · Physical Review A · doi:10.1103/physreva.86.062329 · Cited by 20 · see citing works
Experimental measurement of collective nonlinear entanglement witness for two qubits
Lemr, K., Bartkiewicz, K., & Černoch, A. (2016) · Physical Review A · doi:10.1103/physreva.94.052334 · Cited by 20 · see citing works
Self-citationEinstein-Podolsky-Rosen correlations and Bell correlations in the simplest scenario
Quan, Q., Zhu, H., Fan, H., & Yang, W. (2017) · Physical Review A · doi:10.1103/physreva.95.062111 · Cited by 19 · cited 1× · see citing works
“(34) Rij = Aij + Bij = Tr(ρ1ρ2�σiσj)+ Tr(ρ1ρ2I4σiσj),”
Constraint Relation Between Steerability and Concurrence for Two‐Qubit States
Fan, X., Yang, H., Ming, F., et al. (2021) · Annalen der Physik · doi:10.1002/andp.202100098 · Cited by 19 · cited 1× · see citing works
“These estimations include comparisons of: (i) entanglement and Bell nonlocality [30–33], (ii) steering and Bell nonlocality [34], as well as (iii) entanglement and steering [35].”
Estimating quantum steering and Bell nonlocality through quantum entanglement in two-photon systems
Yang, H., Zhao, F., Fan, X.-G., Ding, Z.-Y., Wang, D., Song, X.-K., Yuan, H., Zhang, C.-J., & Ye, L. (2021) · Optics Express · doi:10.1364/oe.430964 · Cited by 14 · see citing works
Bartkiewicz, K., & Chimczak, G. (2018) · Physical Review A · doi:10.1103/physreva.97.012107 · Cited by 7 · cited 1× · see citing works
“, measuring collective nonlinear witnesses of entanglement [51, 52], Bell nonlocality measure [53], or diagnosing an entanglement-swapping protocol.”
BackgroundSelf-citationExperimental Diagnostics of Entanglement Swapping by a Collective Entanglement Test
Trávníček, V., Bartkiewicz, K., Černoch, A., & Lemr, K. (2020) · Physical Review Applied · doi:10.1103/physrevapplied.14.064071 · Cited by 6 · see citing works
Self-citationExperimental detection of quantum steerability based on the critical radius in an all-optical system
Fan, X.-G., Zhao, F., Yang, H., Ding, Z.-Y., Wang, D., & Ye, L. (2023) · Physical Review A · doi:10.1103/physreva.107.012419 · Cited by 3 · cited 1× · see citing works
“[46], where it was shown experimentally that a critical steering radius is the most powerful among practical steering indicators.”
Background
Flagged first, then by citations
5 of the 75 references couldn’t be matched to a known paper.
Cited by
Sorted by citations
Kadlec, J., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2023) · Optics Express · doi:10.1364/oe.506169 · Cited by 9 · see citing works
“[22,23], we have constructed a fundamentally new setup, which enabled us to experimentally implement an Asbóth et al. entanglement potential [18] (specifically we studied the concurrence potential) and the two recently proposed potentials for other types of quantum correlations for single-qubit…”
MethodSelf-citationAsymmetric bidirectional quantum controlled teleportation via a seven-qubit Werner-like mixed state
Taufiqi, M., Purwanto, A., Yuwana, L., Muniandy, S. V., Al-Amin, M., Prabowo, A. A., & Subagyo, B. A. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad42dc · Cited by 8 · see citing works
Experimental relative entanglement potentials of single-photon states
Kadlec, J., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2024) · Physical Review A · doi:10.1103/physreva.110.023720 · Cited by 6 · see citing works
Self-citationEntanglement, quantum steering, and Bell nonlocality in the Tavis–Cummings system
Ye, B. (2024) · Chinese Journal of Physics · doi:10.1016/j.cjph.2024.09.040 · Cited by 2 · see citing works
Aljuaydi, F., Zidan, N., & Mohamed, A. ‐. A. (2024) · Alexandria Engineering Journal · doi:10.1016/j.aej.2024.07.050 · Cited by 2 · see citing works
Allhibi, H., Alotaibi, M., Aljuaydi, F., & Mohamed, A. A. (2025) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-025-06593-6 · Cited by 1 · see citing works
Deep-learned classification of quantum correlations from collective measurements
Soubusta, J., Černoch, A., & Lemr, K. (2025) · Physics Letters A · doi:10.1016/j.physleta.2025.130911 · Cited by 2 · see citing works
Self-citationMohamed, A. A., Jaradat, E. K., Aldosari, F. M., & Hessian, H. A. (2025) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2025.116396 · Cited by 1 · see citing works
Deepak, D., & Chatterjee, A. (2024) · Physica Scripta · doi:10.1088/1402-4896/ad6ebd · Cited by 1 · see citing works
Optimizing Entanglement in Two‐Qubit Systems
Luna-Hernández, S., Quintana, C., & Rosas-Ortiz, Ó. (2025) · Mathematical Methods in the Applied Sciences · doi:10.1002/mma.10734
“Indeed, in [27, 29], states (13) are prepared for various values of the mixing parameter (cid:23) , so that concurrence (cid:2)(cid:6)(cid:4)(cid:12)(cid:0)(cid:7) (cid:2) (cid:0)(cid:6)’(cid:2)(cid:7) is measured with good agreement of (28).”
Discord-Enhanced Quantum Key Distribution in Noisy Mixed-State ChannelsPreprint
Alkurkushi, S. M., & Algabri, M. N. A. (2025) · Research Square · doi:10.21203/rs.3.rs-8202745/v1
Bell Nonlocality and EPR Steering Decay in Dephasing Hyperfine Spins
Berrada, K., & Bougouffa, S. B. (2025) · Axioms · doi:10.3390/axioms14120908
“…expressions and conducting numerical simulations, we identify Bell nonlocality as the most fragile correlation, followed by steering and purity, and introduce a three-dimensional analysis of Werner states to pinpoint critical purity thresholds for Bell inequality violations under noise [51].”
Experimentally Self-Testing Partially Entangled Two-Qubit States on an Optical Platform
Zhao, X., Yang, Y.-H., Zhao, L.-M., & Luo, M.-X. (2026) · Entropy · doi:10.3390/e28010079
Mohamed, A.-B. A., Jaradat, E. K., Alotaibi, A. M., & Khedr, A. N. (2026) · International Journal of Theoretical Physics · doi:10.1007/s10773-026-06264-x
Mohamed, A.-B. A., Jaradat, E. K., Alharbi, S. S., & Hashem, M. (2026) · International Journal of Theoretical Physics · doi:10.1007/s10773-025-06244-7
Mohamed, A.-B. A., Jaradat, E. K., Khedr, A. N., & Alharbi, S. S. (2026) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-026-07607-7
Kédim, I., Jaradat, E. K., Bouteraa, Y., & Mohamed, A. ‐. A. (2026) · Chinese Journal of Physics · doi:10.1016/j.cjph.2026.06.038
- Authors
- Abo, S., Soubusta, J., Jiráková, K., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A.
- Affiliations
- Adam Mickiewicz University in Poznań (PL)
- Palacký University Olomouc (CZ)
- FZU - Institute of Physics of the Czech Academy of Sciences (CZ)
- Corresponding author
- Soubusta, Jan
- Miranowicz, Adam
- ORCID
- Venue
- Scientific Reports
- Published
- 2023-05-26
- Volume
- 13
- Issue
- 1
- Pages
- 8564-8564
- ISSN
- 2045-2322 (ISSN-L)
- PMC
- PMC10220071
- OpenAlex
- W4378473165
- Semantic Scholar
- 0e90f1b1e3e8cbbfd5cc7a2252ac15531a54392a
- Cited by
- 17
- References
- 75
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 5 · 2023: 1
- FWCI
- 1.51
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Scientific Reports (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- PubMed Central (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- Polish National Science Centre (DEC-2019/34/A/ST2/00081)
- 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
- Werner states, quantum entanglement, quantum steering, Bell nonlocality, two-qubit states, white noise, correlation matrix, Stokes parameters, quantum witness
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.
Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-13.
Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-13.
Cited sources are checked by 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.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
