Quantum Correlations are Tightly Bound by the Exclusivity Principle

Yan, Bin

doi:10.1103/physrevlett.110.260406

Cited by 59 publications

(73 citation statements)

References 37 publications

(77 reference statements)

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“…First, we have shown that the E principle singles out the set of the quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. This result goes beyond the one presented by Yan in [23], since using the same assumptions we have shown that the E principle singles out the entire set of quantum correlations and not just its maximum.…”

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confidence: 45%

“…Another evidence of the strength of the E principle was recently found by Yan [23]. By exploiting Lemma 1 in [34], Yan has proven that, if all correlations predicted by QT for an experiment with exclusivity graph G are reachable in nature, then the E principle singles out the maximum value of the correlations produced by an experiment whose exclusivity graph is the complement of G, denoted as G.…”

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confidence: 96%

“…A second approach consists of identifying principles that explain the set of quantum nonlocal correlations [6][7][8][9][10][11][12][13][14]. The third approach consists of identifying principles that explain the set of quantum contextual correlations [15][16][17][18][19] without restrictions imposed by a specific experimental scenario [20][21][22][23].…”

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confidence: 99%

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Exclusivity principle forbids sets of correlations larger than the quantum set

2014

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We show that the exclusivity (E) principle singles out the set of quantum correlations associated to any exclusivity graph assuming the set of quantum correlations for the complementary graph. Moreover, we prove that, for self-complementary graphs, the E principle, by itself (i.e., without further assumptions), excludes any set of correlations strictly larger than the quantum set. Finally, we prove that, for vertex-transitive graphs, the E principle singles out the maximum value for the quantum correlations assuming only the quantum maximum for the complementary graph. This opens the door for testing the impossibility of higher-than-quantum correlations in experiments. Introduction.-One of the most seductive scientific challenges in recent times is deriving quantum theory (QT) from first principles. The starting point is assuming general probabilistic theories allowing for correlations that are more general than those that arise in QT, and the goal is to find principles that pick out QT from this landscape of possible theories.

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Exclusivity principle forbids sets of correlations larger than the quantum set

2014

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“…The problem of whether or not the E principle (complemented by some assumptions) can explain all the quantum limits of the correlations between the outcomes of comeasurable sharp measurements is still open. However, taking into account the earlier successful predictions of the E principle [18][19][20][21][22][23] and the evidences of failure of other approaches [8][9][10], the result presented here promotes the E principle as the best option for understanding the limits of quantum contextual and nonlocal correlations. This apparent fundamental role of the E principle in QT is also supported by some recent results aiming to understand QT from fundamental physical principles [15,27,28].…”

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confidence: 99%

“…Two events are equivalent when they correspond to indistinguishable states. Two events are exclusive when there is a sharp measurement that perfectly distinguishes between them.The exclusivity (E) principle [18][19][20][21][22][23] states that any set of m pairwise exclusive events is m-wise exclusive. According to Kolmogorov's axioms of probability, the sum of the…”

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Exclusivity principle and the quantum bound of the Bell inequality

Cabello

2014

Phys. Rev. A

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We show that, for general probabilistic theories admitting sharp measurements, the exclusivity principle together with two assumptions exactly singles out the Tsirelson bound of the Clauser-Horne-Shimony-Holt Bell inequality.Introduction.-Quantum theory (QT) is arguably the most accurate scientific theory of all times. Nevertheless, despite its mathematical simplicity, its fundamental principles are still unknown. In the quest for these principles, a key question is why QT is exactly as nonlocal [1] and contextual [2] as it is.There are two different approaches to answer this question. On one hand, the "black box" approach, which focuses on correlations among the outcomes of measurements in multipartite scenarios. This approach makes no assumptions on the internal working of the measurement devices (which are treated as black boxes) and pays no attention to the postmeasurement state of the system (since measurements are treated as if they were demolition measurements). Within this approach, it has been proven that the principles of information causality [3] and macroscopic locality [4], complemented by some assumptions, single out the maximum quantum violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality [5,6] (i.e., the Tsirelson bound [7]). However, it has also been proven that these principles cannot exclude extremal nonlocal boxes prohibited in QT in the three-party, two-outcome, two-setting or (3, 2, 2) scenario [8,9]. Moreover, by its very definition, the black box approach cannot explain quantum contextual correlations [2]. In addition, there is increasing evidence that the black box approach, with independence of the principle invoked, cannot explain even quantum nonlocal correlations [10].On the other hand, the "sharp measurements," "graphtheoretic," or "contextuality" approach [11][12][13] focus on correlations among the outcomes of sharp measurements. For general probabilistic theories (GPTs), sharp measurements are nondemolition measurements that are repeatable and cause minimal disturbance [14,15]. In QT, sharp measurements are projective measurements [16]. In QT, generalized measurements are represented by positive operator-valued measures. However, in QT, any generalized measurement can always be implemented as a sharp measurement on the system and the environment [17].Within the sharp measurements approach, an "event" is defined as the postmeasurement state of the system after a sharp measurement. Two events are equivalent when they correspond to indistinguishable states. Two events are exclusive when there is a sharp measurement that perfectly distinguishes between them.The exclusivity (E) principle [18][19][20][21][22][23] states that any set of m pairwise exclusive events is m-wise exclusive. According to Kolmogorov's axioms of probability, the sum of the

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Semi-classical Response of Solids to Electromagnetic Fields

Stöhr

2023

Springer Tracts in Modern Physics

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Quantum Correlations are Tightly Bound by the Exclusivity Principle

Cited by 59 publications

References 37 publications

Exclusivity principle forbids sets of correlations larger than the quantum set

Exclusivity principle forbids sets of correlations larger than the quantum set

Exclusivity principle and the quantum bound of the Bell inequality

Semi-classical Response of Solids to Electromagnetic Fields

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