Exclusivity principle forbids sets of correlations larger than the quantum set (original) (raw)

Basic exclusivity graphs in quantum correlations

Physical Review A, 2013

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.

Bounding quantum theory with the exclusivity principle in a two-city experiment

Why do correlations between the results of measurements performed on physical systems violate Bell and other non-contextuality inequalities up to some specific limits but not beyond them? The answer may follow from the observation that in quantum theory, unlike in other theories, whenever there is an experiment to measure A simultaneously with B, another to measure B with C, and another to measure A with C, 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: the sum of the probabilities of any set of pairwise exclusive events cannot exceed 1 , which, surprisingly, explains the set of quantum correlations in some fundamental scenarios . A problem opened in is whether the E principle explains the maximum quantum violation of the Bell-CHSH inequality [1, 2] and quantum correlations in other scenarios. 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 a laboratory in Stockholm and, to demonstrate independence, the non-contextuality inequality experiment on single photons' orbital angular momentum states in a laboratory in Rome. The observed results provide the first experimental evidence that the E principle determines the limits of quantum correlations for both scenarios and prove that hypothetical superquantum 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.

Quantum Correlations Require Multipartite Information Principles

Physical Review Letters, 2011

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 non-trivial 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 single out 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.

Quantum Correlations Bell's Theorem

Quantum theory predicts the existence of so-called tripartite-entangled states, in which three quantum particles are related in a way that has no counterpart in classical physics. [48] Physicists from Swansea University are part of an international research collaboration which has identified a new technique for testing the quality of quantum correlations. [47] These insights may prove useful for the development of future theories unifying quantum mechanics and gravity." [46] Physicists at the University of Innsbruck are proposing a new model that could demonstrate the supremacy of quantum computers over classical supercomputers in solving optimization problems. [45] Using data from the CMS experiment there, the researchers studied the entropy resulting from entanglement within the proton. [44]

Experimental Evidence for Bounds on Quantum Correlations

Physical Review Letters, 2004

] to test the bounds of quantum correlation. As expected from the theory we found that, for certain choices of local observables, Cirel'son's bound of the Clauser-Horne-Shimony-Holt inequality ($2\sqrt{2}$) is not reached by any quantum states.

Classical Physics and the Bounds of Quantum Correlations

Physical Review Letters, 2016

A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract correlation scenario with compatible measurements, models based on classical waves produce probability distributions indistinguishable from those of quantum theory and, therefore, share the same bounds. We demonstrate this finding by implementing classical microwaves that propagate along meter-size transmission-line circuits and reproduce the probabilities of three emblematic quantum experiments. Our results show that the "quantum" bounds would also occur in a classical universe without quanta. The implications of this observation are discussed.

Multigraph approach to quantum non-locality

Journal of Physics A: Mathematical and Theoretical, 2014

Non-contextuality (NC) and Bell inequalities can be expressed as bounds Ω for positive linear combinations S of probabilities of events, S ≤ Ω. Exclusive events in S can be represented as adjacent vertices of a graph called the exclusivity graph of S. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel-Lovász-Schrijver theta body of the exclusivity graph. Then, one can easily compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing S over the theta body and calculating the Lovász number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. Here we show that, for any given N-partite Bell inequality, an edge-coloured multigraph composed of N single-colour graphs can be used to encode the relationships of exclusivity between each party's parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovász number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for I 3 , I 3322 and the three bipartite Bell inequalities whose exclusivity graph is a pentagon. The multigraph-theoretical approach introduced here may remove some obstacles in the program of explaining quantum correlations from first principles.

Extremal quantum correlations: Experimental study with two-qubit states

Physical Review A, 2011

We explore experimentally the space of two-qubit quantum correlated mixed states, including frontier ones as defined by the use of quantum discord and von Neumann entropy. Our experimental setup is flexible enough to allow for the high-quality generation of a vast variety of states. We address quantitatively the relation between quantum discord and a recently suggested alternative measure of quantum correlations. PACS numbers: 42.50.Dv,03.67.Bg,42.50.Ex Entanglement, "the characteristic trait of quantum mechanics" according to the words of E. Schrödinger [1], is universally recognized as the key resource in the processing of quantum information and an important tool for the implementation of quantum communication and quantum-empowered metrology . Yet, entanglement does not embody the unique way in which non-classical correlations can be set among the elements of a composite system. When generic mixed states are considered, quantum correlations (QCs) are no longer synonymous of entanglement: Other forms of stronger-thanclassical correlations exist and can indeed be enforced in the state of a multipartite mixed system. However, a general consensus on the measure of quantum correlations is still far from having been found. Among the quantifiers proposed so far, quantum discord [3] (D) occupies a prominent position and enjoys a growing popularity within the community working on quantum information science due to its alleged relevance in the model for deterministic quantum computation with one qubit , extendibility to some important classes of infinitedimensional systems [6] and peculiar role in open-system dynamics . Recently, some attempts at providing an operational interpretation to discord have been reported .

Unified View of Quantum and Classical Correlations

Physical Review Letters, 2010

We discuss the problem of separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to put all correlations on an equal footing. Entanglement and dissonance, whose definition is introduced here, jointly belong to what is known as quantum discord. Our methods are completely applicable for multipartite systems of arbitrary dimensions. We investigate additivity relations between different correlations and show that dissonance may be present in pure multipartite states.