# Locally distinguish unextendible product bases by efficiently using entanglement resource

## TL;DR

This paper develops efficient protocols for local discrimination of unextendible product bases (UPB) using less entanglement, expanding understanding of entanglement's role in quantum state distinguishability.

## Contribution

It introduces new protocols for distinguishing UPB in various dimensions with reduced entanglement resources, generalizing previous methods.

## Key findings

- Protocols for UPB in 5x5 using different entanglement resources
- Generalization of methods for odd-dimensional UPB in dxd
- Distinguishing UPB in even-dimensional systems with multiple low-dimensional entanglement

## Abstract

Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone, can always be locally distinguished using quantum teleportation with enough entanglement resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following open question: how to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement resource. In this paper, we first present two protocols to locally distinguish a set of unextendible product bases (UPB) in $5\otimes 5$ by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in $d\otimes d$, where $d$ is odd and $d\geqslant 3$. Furthermore, for a class of UPB in $d\otimes d$, where $d$ is even and $d\geqslant 4$, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently, and also reveal the phenomenon of less nonlocality with more entanglement.