Discriminating mirror symmetric states with restricted contextual advantage

TL;DR

This paper investigates the conditions under which quantum contextual advantage can be used to discriminate mirror-symmetric quantum states, revealing that such advantage is generally available for two states but limited for three states depending on prior probabilities.

Contribution

The work extends previous results by analyzing discrimination of three mirror-symmetric states and identifying the specific prior probability range where contextual advantage applies.

Findings

Contextual advantage exists for two states at any prior probability.

For three mirror-symmetric states, advantage is limited to certain prior probabilities.

Discrimination of quantum states can be optimized using contextuality.

Abstract

The generalized notion of noncontextuality provides an avenue to explore the fundamental departure of quantum theory from a classical explanation. Recently, extracting a different form of quantum advantage in various information processing tasks has received an upsurge of interest. In a recent work [D. Schmid and R. W. Spekkens, Phys. Rev. X 8, 011015 (2018)] it has been demonstrated that discrimination of two nonorthogonal pure quantum states entails contextual advantage when the states are supplied with equal prior probabilities. We generalized the work to arbitrary prior probabilities as well as to three arbitrary mirror-symmetric states. We show that the contextual advantage can be obtained for any value of prior probability when only two quantum states are present in the task. But surprisingly, in the case of three mirror-symmetric states, the contextual advantage is available only for a restrictive range of prior probabilities with which the states are prepared.