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arXiv · 2207.11183

Systematic construction of quantum contextuality scenarios with rank advantage

Pascal Höhn·Zhen-Peng Xu·Matthias Kleinmann
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Abstract

A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement projectors are assumed to be rays, that is, of unit rank. Only recently a contextuality scenario has been identified where state-independent contextuality requires measurements with projectors of rank two. Using the disjunctive graph product, we provide a systematic method to construct contextuality scenarios which require non-unit rank. We construct explicit examples requiring ranks greater than rank one up to rank five.

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Pascal Höhn, Zhen-Peng Xu, Matthias Kleinmann. 2022-07-22. Systematic construction of quantum contextuality scenarios with rank advantage. https://arxiv.org/abs/2207.11183

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