Why superquantum, no-signaling correlations cannot exist

The idea that nonlocal correlations stronger than quantum correlations between two no-signaling systems could “theoretically” exist is based on an incorrect statistical interpretation of the no-signaling condition. This article shows that any physically realizable no-signaling “box” involving local incompatible observables indeed requires to be described in a noncommutative, quantum-like language of operators, which leads to the derivation of the Tsirelson bound and then contradicts this idea.

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Quantum Mechanics and Global Determinism

Quanta ◽

10.12743/quanta.v7i1.76 ◽

2018 ◽

Vol 7 (1) ◽

pp. 40 ◽

Cited By ~ 5

Author(s):

Emily Christine Adlam

Keyword(s):

Quantum Mechanics ◽

Quantum Correlations ◽

Deterministic Theory ◽

No Signaling ◽

Open Question ◽

Global Determinism

It is proposed that certain features of quantum mechanics may be perspectival effects, which arise because experiments performed on locally accessible variables can only uncover a certain subset of the correlations exhibited by an underlying deterministic theory. This hypothesis is used to derive the no-signaling principle, thus resolving an open question regarding the apparently fine-tuned nature of quantum correlations. Some potential objections to this approach are then discussed and answered.Quanta 2018; 7: 40–53.

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Quantum limit of genuine tripartite correlations by bipartite extremality

International Journal of Quantum Information ◽

10.1142/s0219749920500148 ◽

2020 ◽

Vol 18 (04) ◽

pp. 2050014

Author(s):

Hiroyuki Ozeki ◽

Satoshi Ishizaka

Keyword(s):

Probability Space ◽

Quantum Correlations ◽

Quantum Limit ◽

Sufficient Criterion ◽

Extremal Points ◽

Chsh Inequality ◽

Nonlocal Correlations ◽

Necessary And Sufficient

The characterization of the extremal points of the set of quantum correlations has attracted wide interest. In the simplest bipartite Bell scenario, a necessary and sufficient criterion for identifying extremal correlations has recently been conjectured, but extremality of tripartite correlations is not well known. In this study, we analyze tripartite extremal correlations in terms of the conjectured bipartite extremal criterion, and we demonstrate that the bipartite part of some extremal correlations satisfies the bipartite criterion, even though they violate Svetlichny’s inequality, and therefore are considered (stronger) genuine tripartite nonlocal correlations. This phenomenon arises from the fact that the conjectured extremal criterion is automatically satisfied when the violation of the Clauser–Horne–Shimony–Holt (CHSH) inequality exceeds a certain threshold, the value of which is given by the maximum CHSH violation at the edges of the probability space. This also suggests the possibility that the extremality of bipartite correlations can be certified by verifying whether the CHSH violation exceeds the threshold.

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Monogamy of non-local quantum correlations

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2008.0149 ◽

2008 ◽

Vol 465 (2101) ◽

pp. 59-69 ◽

Cited By ~ 91

Author(s):

Ben Toner

Keyword(s):

Probability Distributions ◽

Bell Inequality ◽

Arbitrary Dimension ◽

Bell Inequalities ◽

Quantum Correlations ◽

Interactive Proof ◽

Proof Systems ◽

Non Local ◽

A New Technique ◽

Tsirelson Bound

We describe a new technique for obtaining Tsirelson bounds, which are upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signalling, we obtain a Tsirelson bound by maximizing over all no-signalling probability distributions. This maximization can be cast as a linear programme. In a setting where three parties, A, B and C, share an entangled quantum state of arbitrary dimension, we (i) bound the trade-off between AB's and AC's violation of the Clauser–Horne–Shimony–Holt inequality and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.

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Quantum Correlations: Challenging the Tsirelson Bound

Quantum Interaction - Lecture Notes in Computer Science ◽

10.1007/978-3-319-28675-4_1 ◽

2016 ◽

pp. 3-11 ◽

Cited By ~ 1

Author(s):

Alexei Grinbaum

Keyword(s):

Quantum Correlations ◽

Tsirelson Bound

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Separation of quantum, spatial quantum, and approximate quantum correlations

Quantum ◽

10.22331/q-2021-01-28-389 ◽

2021 ◽

Vol 5 ◽

pp. 389

Author(s):

Salman Beigi

Keyword(s):

Mathematical Model ◽

Hilbert Spaces ◽

Quantum Correlations ◽

Quantum Measurements ◽

Finite Dimensional ◽

Nonlocal Correlations ◽

Local Quantum

Quantum nonlocal correlations are generated by implementation of local quantum measurements on spatially separated quantum subsystems. Depending on the underlying mathematical model, various notions of sets of quantum correlations can be defined. In this paper we prove separations of such sets of quantum correlations. In particular, we show that the set of bipartite quantum correlations with four binary measurements per party becomes strictly smaller once we restrict the local Hilbert spaces to be finite dimensional, i.e., Cq(4,4,2,2)≠Cqs(4,4,2,2). We also prove non-closure of the set of bipartite quantum correlations with four ternary measurements per party, i.e., Cqs(4,4,3,3)≠Cqa(4,4,3,3).

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Relativistic independence bounds nonlocality

Science Advances ◽

10.1126/sciadv.aav8370 ◽

2019 ◽

Vol 5 (4) ◽

pp. eaav8370 ◽

Cited By ~ 8

Author(s):

Avishy Carmi ◽

Eliahu Cohen

Keyword(s):

Quantum Mechanics ◽

Quantum Correlations ◽

Physical Principle ◽

Quantum Nonlocality ◽

Measuring Instruments ◽

Uncertainty Relations ◽

The Past ◽

Nonlocal Correlations

If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. Here, it is shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we identify a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters’ choices of measuring instruments. We prove that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers.

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QUANTUM NONLOCAL BOXES EXHIBIT STRONGER DISTILLABILITY

Modern Physics Letters A ◽

10.1142/s0217732313300127 ◽

2013 ◽

Vol 28 (17) ◽

pp. 1330012

Author(s):

PETER HØYER ◽

JIBRAN RASHID

Keyword(s):

Quantum Correlations ◽

Status Quo ◽

Quantum Nonlocality ◽

Semidefinite Program ◽

Adaptive Protocol ◽

Nonlocal Correlations ◽

The Status ◽

Strong Motivation ◽

Repeated Applications ◽

Nonlocal Box

The hypothetical nonlocal box (NLB) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the NLB. Motivated by the limited distillability of NLBs, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (qNLBs). We propose a new protocol for distillation and show that it asymptotically distills a class of correlated quantum nonlocal boxes to the value [Formula: see text], whereas in contrast, the optimal non-adaptive parity protocol for classical nonlocal boxes asymptotically distills only to the value 3.0. We show that our protocol is an optimal non-adaptive protocol for 1, 2 and 3 qNLB copies by constructing a matching dual solution for the associated primal semidefinite program (SDP). We conclude that qNLBs are a stronger resource for nonlocality than NLBs. The main premise that develops from this conclusion is that the NLB model is not the strongest resource to investigate the fundamental principles that limit quantum nonlocality. As such, our work provides strong motivation to reconsider the status quo of the principles that are known to limit nonlocal correlations under the framework of qNLBs rather than NLBs.

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CLASSICAL, QUANTUM AND SUPERQUANTUM CORRELATIONS

International Journal of Modern Physics B ◽

10.1142/s0217979213450112 ◽

2012 ◽

Vol 27 (01n03) ◽

pp. 1345011

Author(s):

GIANCARLO GHIRARDI ◽

RAFFAELE ROMANO

Keyword(s):

Quantum Mechanics ◽

Quantum Correlations ◽

Quantum Limit ◽

Nonlocal Correlations ◽

Classical Quantum ◽

Physical Principles

A deeper understanding of the origin of quantum correlations is expected to allow a better comprehension of the physical principles underlying quantum mechanics. In this work, we reconsider the possibility of devising "crypto-nonlocal theories", using a terminology firstly introduced by Leggett. We generalize and simplify the investigations on this subject which can be found in the literature. At their deeper level, such theories allow nonlocal correlations which can overcome the quantum limit.

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Why the Tsirelson Bound? Bub’s Question and Fuchs’ Desideratum

Entropy ◽

10.3390/e21070692 ◽

2019 ◽

Vol 21 (7) ◽

pp. 692 ◽

Cited By ~ 1

Author(s):

William Stuckey ◽

Michael Silberstein ◽

Timothy McDevitt ◽

Ian Kohler

Keyword(s):

Information Theory ◽

Special Relativity ◽

Reference Frame ◽

Quantum Correlations ◽

Quantum Information Theory ◽

Quantum States ◽

The World ◽

Preferred Reference Frame ◽

Bell Basis ◽

Tsirelson Bound

To answer Wheeler’s question “Why the quantum?” via quantum information theory according to Bub, one must explain both why the world is quantum rather than classical and why the world is quantum rather than superquantum, i.e., “Why the Tsirelson bound?” We show that the quantum correlations and quantum states corresponding to the Bell basis states, which uniquely produce the Tsirelson bound for the Clauser–Horne–Shimony–Holt (CHSH) quantity, can be derived from conservation per no preferred reference frame (NPRF). A reference frame in this context is defined by a measurement configuration, just as with the light postulate of special relativity. We therefore argue that the Tsirelson bound is ultimately based on NPRF just as the postulates of special relativity. This constraint-based/principle answer to Bub’s question addresses Fuchs’ desideratum that we “take the structure of quantum theory and change it from this very overt mathematical speak ... into something like [special relativity].” Thus, the answer to Bub’s question per Fuchs’ desideratum is, “the Tsirelson bound obtains due to conservation per NPRF”.

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