Pith. sign in

REVIEW 5 minor 45 references

All tight correlation Bell inequalities have quantum violations

T0 review · 0 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper proves that every nontrivial tight correlation Bell inequality is violated by quantum entanglement.

desk verdict A correct and significant answer to Gill's question for XOR games: no-quantum-advantage correlation Bell inequalities are never facets, so all nontrivial tight ones are quantum violated. read the letter →

arxiv 1908.06669 v1 pith:FDUV3RYC submitted 2019-08-19 quant-ph math-phmath.MP

Llorenç Escolà-Farràs , John Calsamiglia , Andreas Winter This is my paper · ORCID
classification quant-phmath-phmath.MP MSC 81P4081P4552B1190C22
keywords BellinequalitiesXORgamesquantumviolationfacet-defininglocalpolytopesemidefiniteprogrammingdualitycorrelationsnon-localcomputation
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

The paper answers a long-open question: must every tight Bell inequality be violated by quantum mechanics? For two-party, binary-outcome correlation inequalities, the answer is yes. A tight inequality is one that defines a facet of the polytope of local classical correlations, so it belongs to any minimal description of the classical boundary. The proof shows geometrically that if an XOR game has no quantum advantage, the face on which classical and quantum maxima coincide has codimension at least two, and so cannot be a facet. The same mechanism shows the set of quantum correlations has no nontrivial facets, leaving only the trivial non-negative probability bounds as facet-defining.

What carries the argument

The central device is the semidefinite-programming dual of the quantum bias of an XOR game. The game matrix $\Phi$ is embedded into a block matrix $\tilde\Phi = \frac{1}{2}\begin{pmatrix}0&\Phi\\ \Phi^T&0\end{pmatrix}$; the quantum bias is the maximum of $\operatorname{tr}(\tilde Q\tilde\Phi)$ over Gram matrices $\tilde Q$ with all diagonal entries equal to 1. The dual introduces diagonal multipliers $t_i$, and strong duality plus complementary slackness imply that at an optimum with equal classical and quantum values, the matrix $\Gamma-\tilde\Phi$ annihilates the optimal classical vector $|s\rangle=|\alpha_c\rangle\oplus|\beta_c\rangle$, where $\Gamma=\sum_i t_i |i\rangle\langle i|$ is strictly positive for exhaustive games. This splits into $\Sigma|\alpha_c\rangle=\Phi|\beta_c\rangle$ and $\Lambda|\beta_c\rangle=\Phi^T|\alpha_c\rangle$, hence $|\beta_c\rangle=F|\alpha_c\rangle$ with $F=\Lambda^{-1}\Phi^T$, a fixed matrix independent of the strategy. The linear constraint leaves only Alice's $m_A$ sign vectors free, and the correlator block contributes at most $\frac{1}{2}m_A(m_A-1)$ dimensions, giving the codimension bound that rules out facets. The same machinery, with the same $F$, applies to optimal quantum strategies and yields the facetlessness of the quantum set.

What would settle it

Search for an exhaustive XOR game with $\xi_Q=\xi_c$ whose optimal classical face has dimension $D-1$ in the full Bell polytope, or dimension $m_A m_B$ in the correlation polytope; the theorem says neither can happen. A direct numerical check on small cases, say $m_A=2$, $m_B=3$, would enumerate all optimal sign vectors and compute the affine dimension of the face, then compare with the bound $\frac{1}{2}m_A(m_A-1)$; if such a face exists, Theorem 1 fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is Theorem 2: every nontrivial tight correlation Bell inequality for bipartite systems with binary outcomes admits a quantum violation. Equivalently, no XOR game whose classical and quantum maximum biases coincide can define a facet of the Bell polytope. Writing the game matrix as $\Phi$, the classical bias is $\xi_c = \max_{\alpha_c,\beta_c} \langle \alpha_c|\Phi|\beta_c\rangle$, and the quantum bias is the optimum of a semidefinite program over Gram matrices with unit diagonal. The proof assumes $\xi_Q=\xi_c$ and uses complementary slackness in the SDP dual to force a linear relation $|\beta_c\rangle = F|\alpha_c\rangle$ between Alice's and Bob's optimal deterministic strategies, with $F=\Lambda^{-1}\Phi^T$ fixed by the dual multipliers. Consequently the face of classical behaviours maximising the inequality is contained in the affine span of Alice's strategy space, whose dimension is at most $m_A + \frac{1}{2}m_A(m_A-1)$; this is far below the facet dimension $D-1$. The same $F$-relation, applied to optimal quantum strategies, bounds the dimension of faces of the quantum correlation set, proving that it has no facets except the trivial inequalities $|c_{xy}|\le 1$.

Load-bearing premise

The proof relies on every question in the game being asked with positive probability; if a question could be ignored, the argument that Bob's strategy is a fixed linear function of Alice's no longer goes through.

Editorial extensions

If this is right

  • Every facet-defining correlation Bell inequality for two parties with binary outcomes is violated by some entangled strategy; there is no exception among tight inequalities.
  • Any XOR game with no quantum advantage defines a face whose codimension is bounded below by an explicit formula in the numbers of inputs, so the classical and quantum regions of the boundary are separated by at least one dimension.
  • Non-local computation games, the canonical examples of no-quantum-advantage games, are never facet-defining; the dimension bound generalises the earlier proof and shows the face is far from being a facet.
  • The convex set of quantum correlations has no nontrivial facets: every exposed face is low-dimensional except for the trivial inequalities $|c_{xy}|\le 1$.
  • Because the codimension bound is strict and explicit, not only facets but also all faces of dimension above $D-\Delta$ must carry a quantum violation, so the result applies to a quantitative neighbourhood of tightness.

Reading between the lines

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

  • Editorial inference: The same complementary-slackness mechanism is likely to transfer to MOD-$q$ XOR-like games with $q$-ary outputs, which the paper names as an open direction; the strict-positivity condition would be the main thing to re-check.
  • Editorial inference: The facetlessness of the quantum correlation set suggests that no single linear inequality can cleanly separate classical from quantum correlations at a maximal face; separations, if any, must be witnessed by lower-dimensional faces or by families of inequalities.
  • Editorial inference: A direct numerical scan of small XOR games with no quantum advantage could test the tightness of the codimension formula and reveal exactly which games saturate the bound, providing a finite catalogue of extremal no-advantage faces.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 5 minor

Summary. The paper studies two-player XOR games with binary outcomes and the associated correlation Bell inequalities. It proves (Theorem 1) that if an exhaustive XOR game has no quantum advantage, the face of the local Bell polytope, and of the correlation polytope, cut out by the corresponding inequality has codimension strictly greater than one, and hence is not a facet. Theorem 2 extends the argument to non-exhaustive games and concludes that every nontrivial tight correlation Bell inequality has a quantum violation, answering Gill's question affirmatively for the correlation polytope. Theorem 3 transfers the geometric statement to the quantum correlation sets: nontrivial XOR games do not define facets of Qcom or Q⊗, and the set Q0 of quantum correlations has no nontrivial facets. The proofs use semidefinite programming duality, complementary slackness, and Tsirelson's characterization of quantum correlators, with full details in the Supplementary Material, including a separate treatment of non-local computation games.

Significance. If correct, this is a clean structural answer to a long-standing question: facet-defining correlation Bell inequalities are exactly the ones that are nontrivially violated by entanglement, apart from the trivial probability-positivity facets |c_xy| ≤ 1. The proof strategy is novel and elegant, deriving linear determinacy of optimal strategies from complementary slackness and then bounding the affine span of the face. The paper also improves on earlier non-local-computation results by giving explicit, asymptotically attainable dimension bounds, and it yields a striking by-product: the quantum correlation set has no nontrivial facets. The manuscript includes a rigorous SDP-duality proof with full supplementary details, and I verified the one step flagged by an initial reading as potentially missing: the strict positivity of the dual multipliers t_i follows from PSDness together with the assumption that the game matrix has no all-zero rows or columns. There are no fitted parameters or circular inputs; the earlier NLC result is cited but independently reproven.

minor comments (5)
  1. [Title and abstract] The title and the first sentence of the abstract claim that every tight correlation Bell inequality has a quantum advantage, omitting the qualifier 'nontrivial' that appears in Theorem 2; as written they are contradicted by the trivial facets |c_xy| ≤ 1, which are tight in the correlation polytope but have no quantum advantage. Please add the qualifier in both places.
  2. [Supplementary Material C, around Eq. (15)] The definition of Γ as (1/2)Σ ⊕ Λ and the subsequent equations Σ|α_c⟩ = Φ|β_c⟩ and Λ|β_c⟩ = Φ^T|α_c⟩ contain an inconsistent factor of 1/2, so the displayed F = Λ^{-1}Φ^T is not the literal consequence of the preceding line; since only linear determinacy is used this is harmless, but the scaling should be fixed for internal consistency.
  3. [Supplementary Material C, after Eq. (14)] The sentence 'by our assumption that Φ has no all-zero rows or columns, we even can conclude that all t_i > 0' is asserted without proof; it follows from the 2x2 principal minor condition t_i t_j ≥ (Φ_ij/2)^2 together with exhaustiveness, so adding a one-line justification would remove a potential concern for the reader.
  4. [Theorem 2 proof, main text] The dimension count for the non-exhaustive case is very compressed: the codimension bound is stated as 'we thus arrive at' without exhibiting the affine-span calculation for the free marginals and the cross terms. Expanding this step, or explicitly referencing a supplementary section that contains it, would make the proof of the titular theorem easier to verify.
  5. [Main text, after Theorem 2] The term 'nontrivial' is used in Theorem 2 but is only characterized in Supplementary Material B; a parenthetical definition in the main text (inequalities other than ±c_xy ≤ 1) would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the proof is a self-contained SDP-duality argument; self-citations are contextual and not load-bearing.

full rationale

The central theorem is proved from Tsirelson's representation and semidefinite programming duality, not from the result it claims. Theorem 1 derives the linear relation |β_c⟩=F|α_c⟩ from complementary slackness under the hypothesis ξ_Q=ξ_c; this is an internal derivation, not an imported conclusion. The citation to Ramanathan et al. [36] is announced as fundamental but the proof in Supplementary C does not rely on it. The earlier NLC non-facet result ([24], [25]) is cited only as background and is independently reconstructed in Supplementary D; it is not an input to Theorem 2. The only terse step flagged by the reader is the strict positivity of the dual multipliers t_i after Eq. (14); although the proof is compressed, positivity is forced: if t_i=0 for an Alice input, PSDness of Diag(t)-Φ̃ would force that row of Φ to vanish, contradicting exhaustiveness. The non-exhaustive extension in Theorem 2 is a counting argument over unconstrained inputs and does not smuggle in the conclusion. The abstract/title omit the qualifier 'nontrivial', a presentation inaccuracy, but the theorem statement in the body is precise. No fitted parameters, no prediction-from-fit, and no load-bearing self-citation chain appear.

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

The paper introduces no free parameters or invented entities. It relies on standard results in convex geometry (polytope faces, affine spans) and semidefinite programming (strong duality, complementary slackness), plus the known characterization of quantum correlations via Tsirelson's theorem. The axioms listed are the load-bearing background results.

assumptions (5)
  • domain assumption Tsirelson's theorem: the optimal quantum bias of an XOR game is given by the SDP (11) over Gram matrices of unit vectors.
    This is a known theorem from Tsirelson (1980) and Wehner (2006); the paper uses it to write the quantum gain as an SDP. It is load-bearing because the complementary slackness analysis is performed on this SDP.
  • standard math Strong duality and complementary slackness for the SDP (11).
    Used to derive the linear relation |α_c⟩ = Σ^{-1}Φ|β_c⟩ and |β_c⟩ = Λ^{-1}Φ^T|α_c⟩ from the equality of primal and dual optima.
  • standard math The affine span of the matrices |α_c⟩⟨α_c| for |α_c⟩ ∈ {±1}^{m_A} is the space of real symmetric matrices with unit diagonal, of dimension m_A(m_A-1)/2.
    Used in Eq. (16) to bound the face dimension in the Bell polytope.
  • domain assumption The Bell polytope for m_A and m_B inputs has dimension D = m_A m_B + m_A + m_B, and the correlation polytope has dimension m_A m_B.
    Standard parameter counting of no-signalling behaviours; sets the facet dimension.
  • standard math Faces of a polytope are exposed; any facet is an exposed face.
    Used in the final step of Theorem 3 to conclude that any purported facet of the quantum set is defined by an XOR game.

how reviews work

0 comments
Cite this review

Pith. "Pith review of All tight correlation Bell inequalities have quantum violations." pith.science (2026). https://pith.science/paper/FDUV3RYC

@misc{pith2026190806669,
  author       = {Pith},
  title        = {Pith review of: All tight correlation Bell inequalities have quantum violations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FDUV3RYC}},
  note         = {Machine review of arXiv:1908.06669}
}
read the original abstract

It is by now well-established that there exist non-local games for which the best entanglement-assisted performance is not better than the best classical performance. Here we show in contrast that any two-player XOR game, for which the corresponding Bell inequality is tight, has a quantum advantage. In geometric terms, this means that any correlation Bell inequality for which the classical and quantum maximum values coincide, does not define a facet, i.e. a face of maximum dimension, of the local Bell polytope. Indeed, using semidefinite programming duality, we prove upper bounds on the dimension of these faces, bounding it far away from the maximum. In the special case of non-local computation games, it had been shown before that they are not facet-defining; our result generalises and improves this. As a by-product of our analysis, we find a similar upper bound on the dimension of the faces of the convex body of quantum correlation matrices, showing that (except for the trivial ones expressing the non-negativity of probability) it does not have facets.

Figures

Figures reproduced from arXiv: 1908.06669 by the authors.

Figure 1
Figure 1. FIG. 1. Three-dimensional schematic of a local correlation [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Representation of a XOR game. The goal is that [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 43 canonical work pages

  1. [1]

    That is, XOR games with quantum equal to clas- sical value do not define a facet of the full Bell poly- tope. Following the same argument for the correlation polytope leads to the codimension ∆ 0≥ MA(mB− mA)+ 1 2mA(mA +1), and this is greater than 1 unless mA =mB = 1, corresponding precisely to the trivial inequalities|cxy|≤ 1. In the Supplementary Materia...

    work page 2017

  2. [2]

    Clauser, Michael A

    John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt. Proposed Experiment to Test Local Hidden-Variable Theories. Physical Review Let- ters, 23(15):880–883, 1969

    work page 1969

  3. [3]

    Experimental Realization of Einstein- Podolsky-Rosen-Bohm gedankenexperiment: A New Violation of Bell’s Inequalities

    Alain Aspect, Philippe Grangier, and G´ erard Roger. Experimental Realization of Einstein- Podolsky-Rosen-Bohm gedankenexperiment: A New Violation of Bell’s Inequalities. Physical Review Let- ters, 49(2):91–94, July 1982

    work page 1982

  4. [4]

    Closing the Door on Einstein and Bohr’s Quantum Debate

    Alain Aspect. Closing the Door on Einstein and Bohr’s Quantum Debate. Physics (APS), 8:123, De- cember 2015

    work page 2015

  5. [5]

    John S. Bell. On the Einstein-Podolsky-Rosen para- dox. Physics, 1:195–200, 1964

    work page 1964

  6. [6]

    Matsuke- vich, Peter Maunz, Steven Olmschenk, David Hayes, Le Luo, T

    Stefano Pironio, Antonio Ac´ ın, Serge Massar, An- toine Boyer de la Giroday, Dzmirty N. Matsuke- vich, Peter Maunz, Steven Olmschenk, David Hayes, Le Luo, T. Andrew Manning, and Chris Monroe. Random numbers certified by Bell’s theorem. Nature, 464(7291):1021–1024, April 2010

    work page 2010

  7. [7]

    Nonlocality and communication complexity

    Harry Buhrman, Richard Cleve, Serge Massar, and Ronald de Wolf. Nonlocality and communication complexity. Reviews of Modern Physics , 82(1):665– 698, March 2010

    work page 2010

  8. [8]

    Self Testing Quan- tum Apparatus

    Dominic Mayers and Andrew Yao. Self Testing Quan- tum Apparatus. Quantum Information and Compu- tation, 4(4):273–286, July 2004

    work page 2004

Show all 45 references
  1. [9]

    Device- Independent Security of Quantum Cryptography against Collective Attacks

    Antonio Ac´ ın, Nicolas Brunner, Nicolas Gisin, Serge Massar, Stefano Pironio, and Valerio Scarani. Device- Independent Security of Quantum Cryptography against Collective Attacks. Physical Review Letters , 98(23):230501, June 2007

    2007

  2. [10]

    Janet Anders and Dan E. Browne. Computational Power of Correlations. Physical Review Letters , 102(5):050502, February 2009

    2009

  3. [11]

    Bell non- locality

    Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Bell non- locality. Reviews of Modern Physics , 86(2):419–478, April 2014

    2014

  4. [12]

    Cirel’son

    Boris S. Cirel’son. Quantum generalizations of Bell’s inequality. Letters in Mathematical Physics , 4(2):93– 100, March 1980

    1980

  5. [13]

    Ivan ˇSupi´ c and Matty J. Hoban. Self-testing through EPR-steering. New Journal of Physics , 18(7):075006, July 2016

    2016

  6. [14]

    Tsirelson

    Boris S. Tsirelson. Some results and problems on quantum Bell-type inequalities. Hadronic Journal Supplement, 8(4):329–345, 1993

    1993

  7. [15]

    Information causality as a physical princi- ple

    Marcin Paw lowski, Tomasz Paterek, Dagomir Kasz- likowski, Valerio Scarani, Andreas Winter, and Marek ˙Zukowski. Information causality as a physical princi- ple. Nature, 461(7267):1101–1104, October 2009

    2009

  8. [16]

    A glance beyond the quantum model

    Miguel Navascu´ es and Harald Wunderlich. A glance beyond the quantum model. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2115):881–890, March 2010

    2010

  9. [17]

    Quantum nonlocality as an axiom

    Sandu Popescu and Daniel Rohrlich. Quantum nonlocality as an axiom. Foundations of Physics , 24(3):379–385, March 1994

    1994

  10. [18]

    Consequences and limits of nonlocal strate- gies

    Richard Cleve, Peter Høyer, Ben Toner, and John Watrous. Consequences and limits of nonlocal strate- gies. In Proceedings of the 19th IEEE Annual Con- ference on Computational Complexity, pages 236–249, June 2004

    2004

  11. [19]

    Bell inequalities holding for all quan- tum states

    Richard Gill. Bell inequalities holding for all quan- tum states. Open Quantum Problems, Problem 26.B ,

  12. [20]

    Ole Krueger and Reinhard F. Werner. Some Open Problems in Quantum Information Theory. arXiv:quant-ph/0504166, 2005

    2005 arXiv

  13. [21]

    can all be phrased as XOR games; and most im- portantly, they provide a characterisation of the cor- relation Bell polytope as will become apparent below. FIG. 2. Representation of a XOR game. The goal is that Alice and Bob output a and b such that a ⊕ b = f(x, y). In an XOR g...

  14. [22]

    Hoban, and Antonio Ac´ ın

    Miguel Navascu´ es, Yelena Guryanova, Matty J. Hoban, and Antonio Ac´ ın. Almost quantum corre- lations. Nature Communications , 6:6288, February 2015

    2015

  15. [23]

    commuting

    presented another case, the multi-party guess your neighbour’s input (GYNI) game, shown to de- fine a tight Bell inequality without quantum violation. Around the same time, it was understood that NLC games never define facets of the Bell polytope [24], though this result was nev...

    1908 arXiv

  16. [24]

    Quantum mechanics: The useful- ness of uselessness

    Andreas Winter. Quantum mechanics: The useful- ness of uselessness. Nature, 466(7310):1053–1054, Au- gust 2010

    2010

  17. [25]

    Tightness of correlation inequalities with no quantum violation

    Ravishankar Ramanathan, Marco T´ ulio Quintino, Ana Bel´ en Sainz, Gl´ aucia Murta, and Remigiusz Au- gusiak. Tightness of correlation inequalities with no quantum violation. Physical Review A, 95(1):012139, January 2017

    2017

  18. [26]

    Short, and Andreas Winter

    Noah Linden, Sandu Popescu, Anthony J. Short, and Andreas Winter. Quantum Nonlocality and Beyond: Limits from Nonlocal Computation. Physical Review Letters, 99(18):180502, October 2007

    2007

  19. [27]

    M´ ethot, Alain Tapp, and Falk Unger

    Gilles Brassard, Harry Buhrman, Noah Linden, Andr´ e A. M´ ethot, Alain Tapp, and Falk Unger. Limit on Nonlocality in Any World in Which Communica- tion Complexity Is Not Trivial. Physical Review Let- ters, 96(25):250401, june 2006

    2006

  20. [28]

    Almeida, Jean-Daniel Bancal, Nicolas Brunner, Antonio Ac´ ın, Nicolas Gisin, and Stefano Pironio

    Mafalda L. Almeida, Jean-Daniel Bancal, Nicolas Brunner, Antonio Ac´ ın, Nicolas Gisin, and Stefano Pironio. Guess Your Neighbor’s Input: A Multipar- tite Nonlocal Game with No Quantum Advantage. Physical Review Letters, 104(23):230404, June 2010

    2010

  21. [29]

    for mA,mB≥ 5 [30], which is why we define Q⊗ to be its closure. By definition, Q⊗ ⊆ Qcom, and while it is open whether the two sets are equal, this would be equivalent to Connes’ long-standing Embed- ding Problem in the theory of von Neumann algebras [31, 32]. The sets of quantu...

  22. [30]

    Paulsen, and Jitendra Prakash

    Ken Dykema, Vern I. Paulsen, and Jitendra Prakash. Non-closure of the Set of Quantum Correlations via Graphs. Communications in Mathematical Physics , 365(3):1125–1142, February 2019. arXiv[quant- ph]:1709.05032

    2019 arXiv

  23. [31]

    Lifting Bell inequalities

    Stefano Pironio. Lifting Bell inequalities. Journal of Mathematical Physics, 46(6):062112, June 2005

    2005

  24. [32]

    Convex Polytopes

    Branko Gr¨ unbaum. Convex Polytopes . Springer- Verlag, Heidelberg New York, 2nd ed. edition, 2003

    2003

  25. [33]

    Hidden Variables, Joint Probability, and the Bell Inequalities

    Arthur Fine. Hidden Variables, Joint Probability, and the Bell Inequalities. Physical Review Letters , 48(5):291–295, February 1982

    1982

  26. [34]

    The set of quantum correlations is not closed

    William Slofstra. The set of quantum correlations is not closed. Forum of Mathematics, Pi , 7:e1, January

  27. [35]

    Greenberger, Michael A

    Daniel M. Greenberger, Michael A. Horne, Ab- ner Shimony, and Anton Zeilinger. Bell’s theorem without inequalities. American Journal of Physics , 58(12):1131–1143, December 1990

    1990

  28. [36]

    Characterizing the Per- formance of XOR Games and the Shannon Capacity of Graphs

    Ravishankar Ramanathan, Alastair Kay, Gl´ aucia Murta, and Pawe l Horodecki. Characterizing the Per- formance of XOR Games and the Shannon Capacity of Graphs. Physical Review Letters , 113(24):240401, December 2014

    2014

  29. [37]

    Junge, M

    M. Junge, M. Navascues, C. Palazuelos, D. Perez- Garcia, V. B. Scholz, and R. F. Werner. Connes’ embedding problem and Tsirelson’s problem. Journal of Mathematical Physics, 52(1):012102, January 2011

    2011

  30. [38]

    About the qwep conjecture

    Narutaka Ozawa. About the qwep conjecture. In- 6 ternational Journal of Mathematics , 15(05):501–530, July 2004

    2004

  31. [39]

    Constructive Generalization of Bell’s Inequalities

    Marcel Froissart. Constructive Generalization of Bell’s Inequalities. Il Nuovo Cimento B , 64(2):241– 251, 1981

    1981

  32. [40]

    Werner and Michael M

    Reinhard F. Werner and Michael M. Wolf. All- multipartite bell-correlation inequalities for two di- chotomic observables per site. Physical Review A , 64(3):032112, 2001

    2001

  33. [43]

    Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities

    Stephanie Wehner. Tsirelson bounds for generalized Clauser-Horne-Shimony-Holt inequalities. Physical Review A, 73(2):022110, February 2006

    2006

  34. [44]

    Tyrell Rockafeller

    R. Tyrell Rockafeller. Convex Analysis, volume 28 of Princeton Math. Series . Princeton University Press, Princeton, 1970. SUPPLEMENT AR Y MA TERIAL A. Quantum bias If Alice and Bob use quantum resources, i.e. a (pos- sibly) entangled state|ψ⟩∈H , with with observables ˆax and...

    1970

  35. [45]

    By parameter counting, it is straightforward to see that dimG0 = 2n−1(2n− 3), and so we get dim F = 1 + 2n−1(2n− 3)∼ 2n−1(2n− 1), matching the upper bound to leading order

  36. [2005]

    https://oqp.iqoqi.univie.ac.at/bell-inequalities- holding-for-all-quantum-states/

  37. [2019]

    arXiv[quant-ph]:1703.08618

    arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.