LOCC distinguishability of unilaterally transformable quantum states

TL;DR

This paper investigates the conditions under which orthogonal bipartite quantum states, especially those specified by local unitaries, can be perfectly distinguished using one-way LOCC, providing examples and conjectures about two-way LOCC limitations.

Contribution

It establishes a link between the distinguishability of states and the distinguishability of their associated unitaries, and provides explicit examples of maximally entangled states that are not perfectly distinguishable by one-way LOCC.

Findings

States specified by local unitaries can be distinguished iff their unitaries are distinguishable by local measurements.

Explicit examples of maximally entangled states in 4, 5, 6 dimensions that are not perfectly distinguishable by one-way LOCC.

Conjecture that certain states cannot be distinguished even with two-way LOCC.

Abstract

We consider the question of perfect local distinguishability of mutually orthogonal bipartite quantum states, with the property that every state can be specified by a unitary operator acting on the local Hilbert space of Bob. We show that if the states can be exactly discriminated by one-way LOCC where Alice goes first, then the unitary operators can also be perfectly distinguished by an orthogonal measurement on Bob's Hilbert space. We give examples of sets of N<=d maximally entangled states in $d \otimes d $ for d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly for d=5,6 our examples consist of four and five states respectively. We conjecture that these states cannot be perfectly discriminated by two-way LOCC.