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arXiv · 1201.5836

Generalized monogamy of contextual inequalities from the no-disturbance principle

Ravishankar Ramanathan·Akihito Soeda·Pawel Kurzynski·Dagomir Kaszlikowski
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Abstract

In this paper we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no-disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs admit a joint probability distribution, we formulate a precise graph-theoretic condition that gives rise to the monogamy of contextuality. We also show how such monogamies arise within quantum theory for a single four-dimensional system and interpret violation of these relations in terms of a violation of causality. These monogamies can be tested with current experimental techniques.

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Ravishankar Ramanathan, Akihito Soeda, Pawel Kurzynski, Dagomir Kaszlikowski. 2012-09-17. Generalized monogamy of contextual inequalities from the no-disturbance principle. https://doi.org/10.1103/physrevlett.109.050404

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