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arXiv:1303.4357 · Physical Review Letters

Quantum Correlations are Tightly Bound by the Exclusivity Principle

Bin Yan

Published Jun 25, 2013• 62 citations
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Abstract

It is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature, based on quantum mechanics. One possible explanation is the "global exclusivity" principle recently discussed in Phys. Rev. Lett. 110, 060402 (2013). In this work we show that this principle actually has a much stronger restriction on the probability distribution. We provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph. Our result implies that the exclusivity principle might be one of the fundamental principles of nature.

DOI
10.1103/physrevlett.110.260406

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It is a fundamental problem in physics of what principle limits the correlations as predicted by our current description of nature, based on quantum mechanics. One possible explanation is the "global exclusivity" principle recently discussed in Phys. Rev. Lett. 110, 060402 (2013). In this work we show that this principle actually has a much stronger restriction on the probability distribution. We provide a tight constraint inequality imposed by this principle and prove that this principle singles out quantum correlations in scenarios represented by any graph. Our result implies that the exclusivity principle might be one of the fundamental principles of nature.
The most promising candidate for being the fundamental principle of quantum contextuality is the Exclusivity principle, which states that the sum of the probabilities of a set of pairwise exclusive events cannot exceed 1. By itself, the Exclusivity principle singles out the maximum quantum value for some important Bell and noncontextuality inequalities. We can get better results if we apply the E principle to more sophisticated scenarios. This happens because this principle exhibits activation effects: a distribution satisfying this principles does not necessarily satisfy it when combined with other distributions. Activation effects can be used to prove that the Exclusivity principle singles out the set of quantum distributions for the most simple noncontextuality inequality. It is still not known if the exclusivity principle solves the problem of explaining quantum contextuality completely, but many results have been proven that support the conjecture that it might. The main purpose of this thesis is to discuss in detail the situations in which the E principle can be used to rule out distributions outside the quantum set.
This work explores the implications of the exclusivity principle (EP) in the context of quantum and postquantum correlations. We first establish a key technical result demonstrating that given the set of correlations for a complementary experiment, the EP restricts the maximum set of correlations for the original experiment to the antiblocking set. Based on it, we can prove our central result: if all quantum behaviors are accessible in Nature, the EP guarantees that no postquantum behaviors can be realized. This can be seen as a generalization of the result of B. Amaral et al. [Phys. Rev. A 89, 030101(R) (2014)], to a wider range of scenarios. It also provides novel insights into the structure of quantum correlations and their limitations.
Why do correlations between the results of measurements performed on physical systems violate Bell and non-contextuality inequalities up to some specific limits? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure AAA simultaneously with BBB, another to measure BBB with CCC, and another to measure AAA with CCC, there is always an experiment to measure all of them simultaneously. This property implies that quantum theory satisfies a seemingly irrelevant restriction called the exclusivity (E) principle which, surprisingly, explains the set of quantum correlations in some fundamental scenarios. An open problem is whether the E principle explains the maximum quantum violation of the Bell-CHSH inequality. Here we show experimentally that the E principle imposes an upper bound to the violation of the Bell-CHSH inequality that matches the maximum predicted by quantum theory. For that, we use the result of an independent experiment testing a specific non-contextuality inequality. We perform both experiments: the Bell-CHSH inequality experiment on polarization entangled states of pairs of photons in Stockholm and, to demonstrate independence, the non-contextuality inequality experiment on single photons' orbital angular momentum states in Rome. The observed results provide the first experimental evidence that the E principle determines the limits of quantum correlations and prove that hypothetical super-quantum violations for either experiment would violate the E principle. This supports the conclusion that the E principle captures a fundamental limitation of nature. If this is true, much of quantum theory trivially follow from merely taking the E principle to be a fundamental truth, and various information-theoretic postulates are also simplified and/or strengthened.
Identifying which correlations among distant observers are possible within our current description of nature, based on quantum mechanics, is a fundamental problem in physics. Recently, information concepts have been proposed as the key ingredient to characterize the set of quantum correlations. Novel information principles, such as information causality or nontrivial communication complexity, have been introduced in this context and successfully applied to some concrete scenarios. We show in this work a fundamental limitation of this approach: no principle based on bipartite information concepts is able to singleout the set of quantum correlations for an arbitrary number of parties. Our results reflect the intricate structure of quantum correlations and imply that new and intrinsically multipartite information concepts are needed for their full understanding.
We show that the maximum quantum violation of the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality is exactly the maximum value satisfying the following principle: The sum of probabilities of pairwise exclusive events cannot exceed 1. We call this principle "global exclusivity," since its power shows up when it is applied to global events resulting from enlarged scenarios in which the events in the inequality are considered jointly with other events. We identify scenarios in which this principle singles out quantum contextuality, and show that a recent proof excluding nonlocal boxes follows from the maximum violation imposed by this principle to the KCBS inequality.
A fundamental problem is to understand why quantum theory only violates some noncontextuality (NC) inequalities and identify the physical principles that prevent higher-than-quantum violations. We prove that quantum theory only violates those NC inequalities whose exclusivity graphs contain, as induced subgraphs, odd cycles of length five or more, and/or their complements. In addition, we show that odd cycles are the exclusivity graphs of a well-known family of NC inequalities and that there is also a family of NC inequalities whose exclusivity graphs are the complements of odd cycles. We characterize the maximum noncontextual and quantum values of these inequalities, and provide evidence supporting the conjecture that the maximum quantum violation of these inequalities is exactly singled out by the exclusivity principle.