Local distinguishability of orthogonal 2\otimes3 pure states

TL;DR

This paper characterizes when orthogonal 2x3 pure states can be distinguished locally, revealing that LOCC can outperform LPCC and highlighting the importance of classical communication rounds in state discrimination.

Contribution

It provides a complete characterization of local distinguishability for 2x3 pure states and demonstrates the superior power of LOCC over LPCC, with implications for quantum communication protocols.

Findings

LOCC can distinguish certain states that LPCC cannot.

Classical communication rounds are essential for perfect discrimination.

A large class of states require multiple rounds of communication for discrimination.

Abstract

We present a complete characterization for the local distinguishability of orthogonal $2\otimes 3$ pure states except for some special cases of three states. Interestingly, we find there is a large class of four or three states that are indistinguishable by local projective measurements and classical communication (LPCC) can be perfectly distinguishable by LOCC. That indicates the ability of LOCC for discriminating $2\otimes 3$ states is strictly more powerful than that of LPCC, which is strikingly different from the case of multi-qubit states. We also show that classical communication plays a crucial role for local distinguishability by constructing a class of $m\otimes n$ states which require at least $2\min\{m,n\}-2$ rounds of classical communication in order to achieve a perfect local discrimination.