Local Quantum Pure-state Identification without Classical Knowledge

TL;DR

This paper investigates the problem of identifying two unknown bipartite pure quantum states using only samples, and demonstrates that optimal identification can be achieved with LOCC measurements.

Contribution

It proves that the maximum success probability for pure-state identification can be attained through LOCC measurements, even without classical knowledge of the states.

Findings

Optimal success probability is achievable with LOCC.

Constructed LOCC-respecting POVM for state identification.

Applicable to entangled bipartite states.

Abstract

Suppose we want to distinguish two quantum pure states. We consider the case in which no classical knowledge on the two states is given and only a pair of samples of the two states is available. This problem is called quantum pure-state identification problem. Our task is to optimize the mean identification success probability, which is averaged over an independent unitary invariant distribution of the two reference states. In this paper, the two states are assumed bipartite states which are generally entangled. The question is whether the maximum mean identification success probability can be attained by means of an LOCC (Local Operations and Classical Communication) measurement scheme. We will show that this is possible by constructing a POVM which respects the conditions of LOCC.