Global restrictions under local state discrimination

Alexander Bernal; Carles Roch I Carceller

REVIEW 3 major objections 5 minor 40 references

Global restrictions under local state discrimination

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The optimal local discrimination probability of a bipartite ensemble bounds its CHSH violation, maximally entangled fidelity, and energy.

desk verdict A useful extension of local discrimination bounds to global properties, but the N>=3 results rest on an unproved monotonicity claim that needs a proof or a conjecture label. read the letter →

arxiv 2411.19619 v4 pith:YQ5IDKY2 submitted 2024-11-29 quant-ph

Carles Roch I Carceller , Alexander Bernal This is my paper · ORCID

classification quant-ph MSC 81P4581P15 PACS 03.67.-a03.65.Ud

keywords localstatediscriminationCHSHinequalityBellnonlocalitymaximallyentangledfidelityenergyboundsemi-device-independentcertificationaxisymmetricstatesquantum

topics The Measurement Problem

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper establishes that a single number—the optimal probability with which two separated parties can tell apart the reduced states in a prepared ensemble—places hard limits on global properties of the shared states. For two pure preparations with overlap δ, the local success probability satisfies p_L^s ≤ (1/2)(1+√(1−δ²)) (Eq. 9), so observing p_L^s fixes a maximal overlap δ; from that, the CHSH winning probability is bounded by Eq. (10). The argument extends to N preparations: if Alice and Bob locally distinguish their shares with probability p_L^s, the ensemble's fidelity with any maximally entangled state is at most Eq. (17), and the expectation value of a global observable such as the energy is bounded below by Eq. (18)–(19). The interest is that global behaviours—non-locality, entanglement fidelity, energy—can be certified from a local distinguishability task alone, which matters for bounding what an entangled adversary can do in quantum cryptography.

What carries the argument

The load-bearing object is the N-state discrimination function p_N^s(δ) = (1/N²)(√(1+(N−1)δ)+(N−1)√(1−δ))² (Eq. 13), together with its inversion: a measured p_L^s fixes a maximum average overlap δ. The paper's axisymmetric family (Eq. 12) saturates this bound through local projections onto the largest eigenvalue of each reduced state, giving the tightest link between local distinguishability and global overlaps. The extremality claim (Eq. 14–15)—equidistant states are the hardest to distinguish among all ensembles with the same minimal overlap—is what turns a concrete family into a universal bound.

What would settle it

Find a set of N pure bipartite states with pairwise overlaps no smaller than δ whose optimal local discrimination success probability exceeds p_N^s(δ), or whose maximal CHSH winning probability exceeds the bound of Eq. (10) for the observed p_L^s; an SDP search over qubit ensembles for N = 3 or 4 would settle it.

Watch

Extended reading notes

Core claim

The paper's central claim is that local state discrimination acts as a universal constraint on global features of a bipartite ensemble. Given an observed local success probability p_L^s, one maps it to a pairwise overlap δ through the optimal discrimination bound for N equidistant pure states (Eq. 13), and then δ bounds the CHSH winning probability (Eq. 10), the maximal fidelity with a maximally entangled state (Eq. 17), and the minimum energy (Eq. 18). The construction relies on the axisymmetric ensemble of Eq. (12), whose partial traces are diagonal and optimally distinguishable locally, and on the assertion (Eq. 14–15) that this equidistant ensemble is extremal: any ensemble with pairwise overlaps at least δ is no more distinguishable. If correct, the direction of reasoning runs purely from local measurements to global restrictions.

Load-bearing premise

The bounds assume that an equidistant ensemble with pairwise overlap δ is the hardest to distinguish among all pure-state ensembles with overlaps at least δ; this monotonicity, stated in Eqs. (14)–(15), is asserted without proof and carries the fidelity and energy bounds.

Editorial extensions

If this is right

Two parties who only measure how well they can discriminate their local shares can place an upper bound on how much they violate CHSH, without ever running the CHSH game.
In a prepare-and-measure protocol, a bounded local discrimination success probability certifies that the shared ensemble cannot have high fidelity with any maximally entangled state in dimension N².
The same bound translates into a lower bound on the expectation of a global observable such as the vacuum-projector energy, so a power-meter-style estimate follows from a local discrimination measurement.
For N > 2 qubit preparations, the results show a gap between CHSH violation and full distinguishability: non-locality is impossible as soon as preparations are not equivalent.
When only overlaps are constrained, local and global measurement strategies achieve the same optimal success/error region; a gap appears only when the preparations are entangled.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The extremality claim of Eqs. (14)–(15) is where the general N bounds hinge; a reader should expect a proof there rather than a heuristic, since a counterexample would shrink the fidelity and energy bounds to the axisymmetric family only.
For mixed-state ensembles the mapping from p_L^s to δ breaks because reduced states need not be pure; a natural extension would replace pure-state overlaps by some mixed-state distinguishability measure and yield looser but still meaningful bounds.
The energy bound suggests a concrete experimental test: in an optical prepare-and-measure setup, measuring local discrimination success of coherent-state encoding should give a lower bound on average photon number, which can be checked independently.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

Here is my read on Roch i Carceller and Bernal. The paper's core idea is genuinely nice: use the optimal local state discrimination success probability to bound global properties of a bipartite ensemble—CHSH violation for two pure states, fidelity with a maximally entangled state, and global energy. The N=2 CHSH trade-off is solid: combining the Helstrom bound with the Verstraete-Wolf spectrum-based CHSH bound gives Eq. (10) cleanly, and Appendix A proves it for arbitrary prior probabilities. That part is a real result, though it follows from known ingredients.

What is new is the N-state picture: the fidelity bound (Eq. 17) and energy bound (Eqs. 18-19) are not in the prior literature, and the local-vs-global measurement comparison in Section VI is a useful observation. The axisymmetric family construction in Appendix B is careful, and Appendix C gives a legitimate proof of the fidelity bound conditional on the overlaps.

The soft spot is exactly where the stress-test lands. The whole N≥3 inversion—observing p_L^s and concluding every pairwise overlap is at most δ—rests on the monotonicity/rigidity claim in Eqs. (14)-(15), which is asserted with a heuristic paragraph, not proven. No citation is supplied, and the supplementary material referenced as [28] does not appear to contain it either. For N=2 the claim follows from Fuchs-van de Graaf and reduced state fidelity, so the two-state results stand. But for N≥3, Eqs. (17)-(19) and the N=3,4 CHSH curves are unsupported at their load-bearing point. It is plausible the claim is true—the equidistant ensemble is the natural extremal case—but it is a nontrivial optimization over Gram matrices with pairwise overlap constraints, and the paper gives no proof.

Minor issues: the numerical SDP section has no code or data, and the N=3,4 CHSH generalization is only computed for the symmetric ensemble, so it is really a conjecture unless the monotonicity is proven. The text gestures at these limitations but does not flag the missing proof explicitly.

Overall, this paper is worth engaging. The two-state result is proven, the framework is interesting, and the gap is a missing proof rather than a demonstrated counterexample. A serious referee could push for a proof of Eqs. (14)-(15) or, failing that, a clear conjecture label plus numerical evidence. I would send it to peer review, with the expectation of a major revision.

Recommendation: accept for serious peer review, conditional on the authors proving or properly flagging the monotonicity claim. I would not cite the N≥3 bounds in my own work until the inversion is settled.

Referee Report

3 major / 5 minor

Summary. The paper investigates a prepare-and-measure scenario in which Charlie prepares N bipartite pure states, and Alice and Bob use fixed local measurements to discriminate them. The authors claim that the optimal local success probability p_L^s restricts global properties of the ensemble: an upper bound on the CHSH winning probability (Eq. (10) for N=2 and extensions for N=3,4), an upper bound on the fidelity with any maximally entangled state (Eq. (17)), and a lower bound on the energy expectation (Eq. (19)). The argument for N=2 combines the Helstrom bound with a spectrum-based CHSH optimization in Appendix A. For general N, the paper constructs an axisymmetric ensemble (Eq. (12)) whose local reduced states are optimally distinguishable, and then invokes a monotonicity statement (Eqs. (14)-(15)) to invert an observed p_L^s into a uniform upper bound on all pairwise global overlaps. A final section compares local versus global discrimination with inconclusive events, using an SDP hierarchy.

Significance. If the main claims are correct, the paper offers a conceptually appealing and potentially useful tool: from a purely local distinguishability measurement one can certify upper bounds on Bell violations and entanglement fidelity, and lower bounds on energy, of an uncharacterized shared ensemble. This is a fresh angle on semi-device-independent certification. The N=2 derivation is rigorous and built on standard tools (Helstrom bound, Verstraete-Wolf CHSH optimization), and Appendix C contains a clean and correct fidelity bound. The numerical SDP in Section VI supports the N=2 trade-off. However, the generalization to N>=3 rests on an unproved monotonicity/rigidity claim that is load-bearing for Eqs. (17) and (19), and the N=3,4 CHSH extension is only computed for the symmetric ensemble. The paper therefore has a valuable core but is not yet complete at its central proof step.

major comments (3)

[Sec. IV, Eqs. (14)-(15)] The monotonicity claim in Eq. (14) is asserted without proof or citation: it states that among all ensembles of N pure states with pairwise overlaps at least δ, the equidistant (axisymmetric) ensemble is the most distinguishable. For N>=3 this is a nontrivial optimization over Gram matrices with pairwise overlap constraints, and it is not obvious that the maximum of the minimal-error success probability is attained by the symmetric ensemble. This claim is load-bearing: it is the only mechanism that converts an observed local success probability p_L^s into a bound on all global overlaps, which is then used to derive Eq. (17) and Eq. (19). Until Eq. (14) is proved (or supported by a citable theorem), the N>=3 fidelity and energy bounds are unsupported.
[Sec. IV, Eq. (15)] The inversion step in Eq. (15) is not logically established. The argument says that if some overlaps are reduced, distinguishability increases, so an ensemble with some overlaps smaller than δ can still reach p_N^s(δ). This does not imply that every ensemble attaining p_N^s(δ) has all overlaps at most δ: an ensemble with one overlap slightly above δ and another overlap well below δ could conceivably have the same overall success probability. The statement 'p_φ^s = p_N^s(δ) ⇒ 〈φ_z|φ_z'⟩ ≤ δ for all z,z' requires proof. This inversion is exactly what allows the authors to feed a single inferred δ into the fidelity bound, so it is a second load-bearing gap in the N>=3 argument.
[Appendix A, Eqs. (A8)-(A11)] The CHSH bound for N=3,4 is derived only for the equidistant ensemble, i.e., under the assumption that all pairwise overlaps equal δ. The text claims that 'this construction works in the general case', but no proof is given that among all ensembles with pairwise overlaps bounded by δ, the symmetric ensemble maximizes the CHSH violation. The eigenvalues in Eq. (A10) are specific to the equidistant Gram matrix. Without an optimality argument over non-symmetric ensembles, Fig. 4 and the associated N=3,4 trade-off statements are not established for arbitrary ensembles with bounded overlaps.

minor comments (5)

[Abstract] The abstract contains a typo: 'maximally entangled sate fidelity' should read 'maximally entangled state fidelity'.
[Appendix A, after Eq. (A7)] The sentence 'coinciding with Eq. (9)' appears to be a cross-reference error: Eq. (A7) is the CHSH winning-probability bound and should be compared with Eq. (7) of the main text, not with the Helstrom bound in Eq. (9).
[Sec. VI] The comparison between local and global discrimination strategies is presented as a numerical observation, but no code or data are provided. Since the Gram-matrix SDP is an outer approximation, the claim that the local and global feasible regions coincide needs either a formal argument or reproducible numerical evidence.
[Sec. IV] The scope is restricted to pure state preparations, but this is not made explicit in the abstract or introduction. The phrase 'N bi-partite pure state preparations' appears only in Section IV; stating the purity assumption earlier would help readers assess the applicability of the bounds.
[Sec. VI, Fig. 3] The two panels of Fig. 3 are labelled 'Free states' and 'Entangled states', but the caption does not explain how these labels correspond to the overlap parameter δ and to the ensemble in Eq. (5). Clarifying the distinction between the two panels would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the bounds are built on external results (Helstrom, Tsirelson, Verstraete-Wolf, Wolkowicz-Styan, Ref. [34]); the unproven monotonicity in Eqs. (14)-(15) is an incompleteness, not a circular reduction.

full rationale

The derivation chain is not circular. In Section III, the observed local success probability is inverted into an overlap bound through the standard Helstrom formula (Eq. 9), which is an external theorem rather than a definitional identity, and the CHSH bound (Eq. 10) follows by composing that with the spectrum-based bound proved in Appendix A using the external Verstraete-Wolf result [39]. The axisymmetric family in Eq. (5) is used only to exhibit tightness. For N>=3, the fidelity and energy bounds (Eqs. 17-19) rest on the overlap-to-fidelity lemma proved in Appendix C via the Wolkowicz-Styan eigenvalue bound [40], and on the inversion p_L^s = p_N^s(delta), where p_N^s(delta) is taken from the independent result [34]. The axisymmetric states of Eq. (12) again serve as a tightness construction, not as the source of the bound. The load-bearing step that is not fully justified is the monotonicity/rigidity assertion in Eqs. (14)-(15): the text argues heuristically that any ensemble with all pairwise overlaps >= delta is no more distinguishable than the equidistant ensemble, and that attaining p_N^s(delta) forces all overlaps <= delta. This is an unproven lemma and therefore a completeness/correctness risk, but it is not circular: p_N^s(delta) is not defined as the maximum over all overlap-constrained ensembles, no parameter is fitted to data, and the claimed implication does not reduce to the definition of any quantity in the paper. Self-citations to [28] point to supplementary proofs that are substantially included in Appendices A-C and are not used as an unverified external authority. The numerical SDP in Section VI is described without code or data, which is a reproducibility concern rather than a circularity. Overall, no step in the paper's own equations makes a prediction equivalent to its input by construction, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The work uses standard quantum information results and two domain assumptions (pure preparations, symmetric local states). The key unproved element is the monotonicity property in Eq. (14)-(15), flagged as an ad-hoc assumption. No invented entities or free parameters are introduced.

assumptions (5)

domain assumption Preparations are pure states: ρ_z = |ψ_z><ψ_z|.
The bounds relate local distinguishability to global overlaps defined for pure states. Mixed-state ensembles are not covered by the main results.
standard math For a state with fixed spectrum, the maximal CHSH violation is achieved by a Bell-diagonal state (Ref [39]).
Used in Appendix A to reduce the CHSH bound to a function of the spectrum of the average state ρ.
standard math For pure states with overlap δ, the local discrimination success probability is at most 1/2(1+sqrt(1-δ^2)), with equality for the family in Eq. (5).
This is the Helstrom bound via trace distance between reduced states; used to invert p_L_s to a bound on δ.
ad hoc to paper Any ensemble of N pure states with pairwise overlaps ≥ δ is no more distinguishable than the equidistant (axisymmetric) ensemble with overlap δ (Eq. 14-15).
Stated without proof or citation in Section IV; load-bearing for associating an observed p_L_s with an upper bound on δ. This is the weakest link in the N-state generalization.
domain assumption The observed local success probability satisfies p_A_s = p_B_s = p_L_s for the ensembles considered.
Stated in Section II as holding within the scope of the work; allows using p_L_s as the single figure of merit.

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Pith. "Pith review of Global restrictions under local state discrimination." pith.science (2026). https://pith.science/paper/YQ5IDKY2

@misc{pith2026241119619,
  author       = {Pith},
  title        = {Pith review of: Global restrictions under local state discrimination},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YQ5IDKY2}},
  note         = {Machine review of arXiv:2411.19619}
}

read the original abstract

We investigate how local distinguishability can restrict global properties of bi-partite states. We begin exploring how non-locality becomes limited by optimal local state discrimination and observe a non-trivial trade-off between the Clauser-Horne-Shimony-Holt (CHSH) violation and success probability of local discrimination. We extend our findings to bounding the maximally entangled sate fidelity and global observables such as the energy. Our results show that optimal local state discrimination can become a powerful tool to limit global behaviours, e.g. from entangled adversaries in quantum cryptography.

Figures

Figures reproduced from arXiv: 2411.19619 by the authors.

**Figure 2.** FIG. 2: Trade-off between CHSH violation and local state [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3: Observable success and error probabilities in a bi-partite two-state discrimination scenario. Global (GLOB) [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4: Trade-off between CHSH violation and local state distinguishability characterized through the state discrimination [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 34 canonical work pages

[28]

Supplementary material for: Global restrictions under local state discrimination

work page
[1]

S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photon. 1, 238 (2009)

2009
[2]

Bae and L.-C

J. Bae and L.-C. Kwek, Quantum state discrimination and its applications, Journal of Physics A: Mathematical and Theo- retical 48, 083001 (2015)

work page 2015
[3]

C. W . Helstrom, Detection theory and quantum mechanics, Information and Control 10, 254 (1967)

work page 1967
[4]

C. W . Helstrom, Detection theory and quantum mechanics (ii), Information and Control 13, 156 (1968)

work page 1968
[5]

C. W . Helstrom, Quantum detection and estimation theory , Journal of Statistical Physics 1, 231 (1969)

1969
[6]

Bae, W .-Y

J. Bae, W .-Y. Hwang, and Y.-D. Han, No-signaling principle can determine optimal quantum state discrimination, Phys. Rev. Lett. 107, 170403 (2011)

work page 2011
[7]

Tavakoli, J

A. Tavakoli, J. Pauwels, E. Woodhead, and S. Pironio, Corre- lations in entanglement-assisted prepare-and-measure sce- narios, PRX Quantum 2, 040357 (2021)

work page 2021

Show all 40 references

[8]

Navascués, K

M. Navascués, K. F . Pál, T . Vértesi, and M. Araújo, Self-testing in prepare-and-measure scenarios and a robust version of wigner’s theorem, Phys. Rev. Lett. 131, 250802 (2023)

2023
[9]

C. H. Bennett and G. Brassard, Quantum cryptography: Pub- lic key distribution and coin tossing, Proceedings of IEEE In- ternational Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175–179. (1984)

1984
[10]

Gisin, G

N. Gisin, G. Ribordy , W . Tittel, and H. Zbinden, Quantum cryptography , Rev. Mod. Phys.74, 145 (2002)

2002
[11]

Pawłowski and N

M. Pawłowski and N. Brunner, Semi-device-independent se- curity of one-way quantum key distribution, Phys. Rev. A84, 010302 (2011)

2011
[12]

Li, Z.-Q

H.-W . Li, Z.-Q. Yin, Y.-C. Wu, X.-B. Zou, S. Wang, W . Chen, G.-C. Guo, and Z.-F . Han, Semi-device-independent random- number expansion without entanglement, Phys. Rev. A 84, 034301 (2011)

2011
[13]

J. B. Brask, A. Martin, W . Esposito, R. Houlmann, J. Bowles, H. Zbinden, and N. Brunner, Megahertz-rate semi-device- independent quantum random number generators based on unambiguous state discrimination, Phys. Rev. Appl. 7, 054018 (2017)

2017
[14]

Roch i Carceller, K

C. Roch i Carceller, K. Flatt, H. Lee, J. Bae, and J. B. Brask, Quantum vs noncontextual semi-device-independent ran- domness certification, Phys. Rev. Lett. 129, 050501 (2022)

2022
[15]

Schmid and R

D. Schmid and R. W . Spekkens, Contextual advantage for state discrimination, Phys. Rev. X 8, 011015 (2018)

2018
[16]

Flatt, H

K. Flatt, H. Lee, C. R. I. Carceller, J. B. Brask, and J. Bae, Contextual advantages and certification for maximum- confidence discrimination, PRX Quantum3, 030337 (2022)

2022
[17]

Roch i Carceller and J

C. Roch i Carceller and J. B. Brask, Contextuality witness inspired by optimal state discrimination, Phys. Rev. A 109, 032202 (2024)

2024
[18]

Brunner, M

N. Brunner, M. Navascués, and T . Vértesi, Dimension wit- nesses and quantum state discrimination, Phys. Rev. Lett. 110, 150501 (2013)

2013
[19]

J. S. Bell, On the einstein podolsky rosen paradox, Physics Physique Fizika 1, 195 (1964)

1964
[20]

Mayers and A

D. Mayers and A. Yao, Quantum cryptography with imperfect apparatus, in Proceedings of the 39th Annual Symposium on Foundations of Computer Science , FOCS ’98 (IEEE Computer Society , USA, 1998) p. 503

1998
[21]

A. Acín, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V . Scarani, Device-independent security of quantum cryptog- raphy against collective attacks, Phys. Rev. Lett. 98, 230501 (2007)

2007
[22]

Colbeck and A

R. Colbeck and A. Kent, Private randomness expansion with untrusted devices, Journal of Physics A: Mathematical and Theoretical 44, 095305 (2011)

2011
[23]

A. Acín, S. Massar, and S. Pironio, Randomness versus non- locality and entanglement, Phys. Rev. Lett. 108, 100402 (2012)

2012
[24]

B. S. Tsirel’son, Quantum analogues of the bell inequalities. the case of two spatially separated domains, Journal of So- viet Mathematics 36, 557 (1987)

1987
[25]

D. Saha, K. Sen, C. Srivastava, and U. Sen, Minimal-error quantum state discrimination versus robustness of entan- glement:more indistinguishability with less entanglement (2024), arXiv:2402.05074 [quant-ph]

2024
[26]

J. F . Clauser, M. A. Horne, A. Shimony , and R. A. Holt, Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett. 23, 880 (1969)

1969
[27]

B. S. Cirel’son, Quantum generalizations of bell’s inequality , Letters in Mathematical Physics 4, 93 (1980)

1980
[29]

Tavakoli, A

A. Tavakoli, A. Pozas-Kerstjens, P . Brown, and M. Araújo, Semidefinite programming relaxations for quantum correla- tions (2024), arXiv:2307.02551 [quant-ph]

2024 arXiv
[30]

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W . K. Wootters, Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels, Phys. Rev. Lett. 70, 1895 (1993)

1993
[31]

Eltschka and J

C. Eltschka and J. Siewert, Negativity as an estimator of en- tanglement dimension, Phys. Rev. Lett.111, 100503 (2013)

2013
[32]

Eltschka, G

C. Eltschka, G. Tóth, and J. Siewert, Partial transposition as a direct link between concurrence and negativity , Phys. Rev. A 91, 032327 (2015)

2015
[33]

Seelbach Benkner, J

M. Seelbach Benkner, J. Siewert, O. Gühne, and G. Sentís, Characterizing generalized axisymmetric quantum states in d× d systems, Phys. Rev. A 106, 022415 (2022)

2022
[34]

Pauwels, S

J. Pauwels, S. Pironio, and A. Tavakoli, Information capacity of quantum communication under natural physical assump- tions (2024), arXiv:2405.07231 [quant-ph]

2024 arXiv
[35]

Y. Wang, I. W . Primaatmaja, E. Lavie, A. Varvitsiotis, and C. C. W . Lim, Characterising the correlations of prepare-and- measure quantum networks, npj Quantum Information5, 17 (2019)

2019
[36]

Navascués, S

M. Navascués, S. Pironio, and A. Acín, A convergent hierar- chy of semidefinite programs characterizing the set of quan- tum correlations, New Journal of Physics10, 073013 (2008)

2008
[37]

C. H. Bennett, D. P . DiVincenzo, C. A. Fuchs, T . Mor, E. Rains, P . W . Shor, J. A. Smolin, and W . K. Wootters, Quantum nonlo- cality without entanglement, Phys. Rev. A 59, 1070 (1999)

1999
[38]

R. F . Werner, Quantum states with einstein-podolsky-rosen correlations admitting a hidden-variable model, Phys. Rev. A 40, 4277 (1989)

1989
[39]

Verstraete and M

F . Verstraete and M. M. Wolf, Entanglement versus bell vi- olations and their behavior under local filtering operations, Phys. Rev. Lett. 89, 170401 (2002)

2002
[40]

Wolkowicz and G

H. Wolkowicz and G. P . Styan, Bounds for eigenvalues using traces, Linear Algebra and its Applications 29, 471 (1980), special Volume Dedicated to Alson S. Householder. 8 Appendix A: CHSH optimal violation In this part of the supplemental material we show that the bound in Eq...

1980

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.

[1] [28]

Supplementary material for: Global restrictions under local state discrimination

work page

[2] [1]

S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photon. 1, 238 (2009)

2009

[3] [2]

Bae and L.-C

J. Bae and L.-C. Kwek, Quantum state discrimination and its applications, Journal of Physics A: Mathematical and Theo- retical 48, 083001 (2015)

work page 2015

[4] [3]

C. W . Helstrom, Detection theory and quantum mechanics, Information and Control 10, 254 (1967)

work page 1967

[5] [4]

C. W . Helstrom, Detection theory and quantum mechanics (ii), Information and Control 13, 156 (1968)

work page 1968

[6] [5]

C. W . Helstrom, Quantum detection and estimation theory , Journal of Statistical Physics 1, 231 (1969)

1969

[7] [6]

Bae, W .-Y

J. Bae, W .-Y. Hwang, and Y.-D. Han, No-signaling principle can determine optimal quantum state discrimination, Phys. Rev. Lett. 107, 170403 (2011)

work page 2011

[8] [7]

Tavakoli, J

A. Tavakoli, J. Pauwels, E. Woodhead, and S. Pironio, Corre- lations in entanglement-assisted prepare-and-measure sce- narios, PRX Quantum 2, 040357 (2021)

work page 2021