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      Continuous-variable nonlocality and contextuality

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          Abstract

          Contextuality is a non-classical behaviour that can be exhibited by quantum systems. It is increasingly studied for its relationship to quantum-over-classical advantages in informatic tasks. To date, it has largely been studied in discrete variable scenarios, where observables take values in discrete and usually finite sets. Practically, on the other hand, continuous-variable scenarios offer some of the most promising candidates for implementing quantum computations and informatic protocols. Here we set out a framework for treating contextuality in continuous-variable scenarios. It is shown that the Fine--Abramsky--Brandenburger theorem extends to this setting, an important consequence of which is that nonlocality can be viewed as a special case of contextuality, as in the discrete case. The contextual fraction, a quantifiable measure of contextuality that bears a precise relationship to Bell inequality violations and quantum advantages, can also be defined in this setting. It is shown to be a non-increasing monotone with respect to classical operations that include binning to discretise data. Finally, we consider how the contextual fraction can be formulated as an infinite linear program, and calculated with increasing accuracy using semi-definite programming approximations.

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          Quantum nonlocality as an axiom

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            A Course in Convexity

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              The sheaf-theoretic structure of non-locality and contextuality

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                Author and article information

                Journal
                20 May 2019
                Article
                1905.08267
                54f18283-63a1-41f7-a131-81dda2a32139

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                27 pages including 6 pages supplemental material, 2 figures
                quant-ph math-ph math.CT math.MP math.PR

                Mathematical physics,Quantum physics & Field theory,Mathematical & Computational physics,Probability,General mathematics

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