Locally distinguishing quantum states with limited classical communication

TL;DR

This paper investigates the ability to distinguish pure orthogonal quantum states using local operations with limited classical communication, comparing the effectiveness of entanglement and multiple copies as resources.

Contribution

It introduces new settings for quantum state discrimination under communication constraints and compares the roles of entanglement and copies as resources.

Findings

Entanglement can enable perfect discrimination where classical communication alone cannot.

Multiple copies of states can sometimes substitute for entanglement in discrimination tasks.

Restrictions on classical communication impact the distinguishability of quantum states.

Abstract

We consider different settings of the task to distinguish pure orthogonal quantum states under local operations and a limited amount of classical communication. In the first setting, the spatially separated parties are allowed to perform only local projective measurements without any classical communication during the measurements. Under such a restricted class of operations, if the states are indistinguishable, then within a second group of settings, the parties are allowed to use an additional resource for the distinguishing. The additional resource is either a pure entangled state or multiple identical copies of the given states. Comparisons between these two types of resources are also done in certain cases. Both probabilistic and perfect discrimination of the states are considered for the second group of settings. Within a third setting, the parties perform local projective measurements with a restriction on the availability of classical communication during the measurements. But in this setting the parties are allowed to use a maximally entangled state as a resource.