Locality and nonlocality in quantum pure-state identification problems

TL;DR

This paper investigates the limits of local operations and classical communication in quantum pure-state identification, showing LOCC can match global success in minimum-error cases but not in unambiguous identification.

Contribution

It demonstrates the conditions under which LOCC schemes can achieve optimal success probabilities in quantum state identification problems.

Findings

LOCC attains global success probability in minimum-error identification.

LOCC's success is less than global in unambiguous identification.

The study focuses on bipartite pure entangled states with single copies.

Abstract

Suppose we want to identify an input state with one of two unknown reference states, where the input state is guaranteed to be equal to one of the reference states. We assume that no classical knowledge of the reference states is given, but a certain number of copies of them are available instead. Two reference states are independently and randomly chosen from the state space in a unitary invariant way. This is called the quantum state identification problem, and the task is to optimize the mean identification success probability. In this paper, we consider the case where each reference state is pure and bipartite, and generally entangled. The question is whether the maximum mean identification success probability can be attained by means of a local operations and classical communication (LOCC) measurement scheme. Two types of identification problems are considered when a single copy of each reference state is available. We show that a LOCC scheme attains the globally achievable identification probability in the minimum-error identification problem. In the unambiguous identification problem, however, the maximal success probability by means of LOCC is shown to be less than the globally achievable identification probability.