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. Briefly, a set of states can be antidistinguished if there exists a measurement on the basis of which one can exclude one of the states as definitely not having been prepared. The Yu-Oh 13 ray contextuality 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. Antidistiguishability-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.