Locality of Orthogonal Product States via Multiplied Copies

TL;DR

This paper investigates how many copies of orthogonal product states are needed for LOCC protocols to distinguish them, providing general bounds applicable to any system and improving understanding of quantum state discrimination.

Contribution

It introduces a general method to determine the number of copies required for LOCC distinguishability of any set of orthogonal product states in bipartite and multipartite systems.

Findings

Seven orthogonal product states can be distinguished with a single copy.

N states are distinguishable with loor;N/4 copies in bipartite systems.

N states are distinguishable with loor;N/4 + 1 copies in multipartite systems.

Abstract

In this paper, we consider the LOCC distinguishability of product states. We employ polygons to analyze orthogonal product states in any system to show that with LOCC protocols, to distinguish seven orthogonal product states, one can exclude four states via a single copy. In bipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $\left \lceil \frac{N}{4} \right \rceil$ copies are allowed, where $\left \lceil l\right \rceil$ for a real number $l$ means the smallest integer not less than $l$. In multipartite systems, this result implies that N orthogonal product states are LOCC distinguishable if $\left \lceil \frac{N}{4}\right \rceil + 1$ copies are allowed. We also give a theorem to show how many states can be excluded via a single copy if we are distinguishing n orthogonal product states by LOCC protocols in a bipartite system. Not like previous results, our result is a general result for any set of orthogonal product states in any system.