Related papers: Systematic construction of quantum contextuality scenarios with rank advantage

Systematic construction of quantum contextuality scenarios with rank advantage

URL: http://arxiv.org/abs/2207.11183v1
Date: Fri, 22 Jul 2022 16:45:18 GMT
Title: Systematic construction of quantum contextuality scenarios with rank advantage
Authors: Pascal H\"ohn, Zhen-Peng Xu, Matthias Kleinmann
Abstract summary: 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. We provide a systematic method to construct contextuality scenarios which require non-unit rank.
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License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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