Local unambiguous discrimination of symmetric ternary states

TL;DR

This paper analyzes when sequential local measurements with one-way communication can optimally discriminate symmetric ternary quantum states, including optical coherent states, providing necessary and sufficient conditions for global optimality.

Contribution

It establishes conditions under which sequential measurements are globally optimal for symmetric ternary states with three-dimensional subsystems, extending understanding beyond binary cases.

Findings

Sequential measurements can be globally optimal for certain symmetric ternary states.

Provided necessary and sufficient conditions for bipartite optimality.

Examples demonstrate cases where local measurements match global optimality.

Abstract

We investigate unambiguous discrimination between given quantum states with a sequential measurement, which is restricted to local measurements and one-way classical communication. If the given states are binary or those each of whose individual systems is two-dimensional, then it is in some cases known whether a sequential measurement achieves a globally optimal unambiguous measurement. In contrast, for more than two states each of whose individual systems is more than two-dimensional, the problem becomes extremely complicated. This paper focuses on symmetric ternary pure states each of whose individual systems is three-dimensional, which include phase shift keyed (PSK) optical coherent states and a lifted version of "double trine" states. We provide a necessary and sufficient condition for an optimal sequential measurement to be globally optimal for the bipartite case. A sufficient condition of global optimality for multipartite states is also presented. One can easily judge whether these conditions hold for given states. Some examples are given, which demonstrate that, despite the restriction to local measurements and one-way classical communication, a sequential measurement can be globally optimal in quite a few cases.