Noncontextuality inequalities from antidistinguishability

Noncontextuality inequalities are usually derived from the distinguishability properties of quantum states, i.e., their orthogonality. Here, we show that antidistinguishability can also be used to derive noncontextuality inequalities. The Yu-Oh 13-ray noncontextuality inequality can be rederived and generalized as an instance of our antidistinguishability method. For some sets of states, the antidistinguishability method gives tighter bounds on noncontextual models than just considering orthogonality, and the Hadamard states provide an example of this. We also derive noncontextuality inequalities based on mutually unbiased bases and symmetric informationally complete positive operator-valued measures. Antidistinguishability based inequalities were initially discovered as overlap bounds for the reality of the quantum state. Our main contribution here is to show that they are also noncontextuality inequalities.

The article was published in: Phys. Rev. A 101, 062113 (24 June 2020)

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.