Entanglement as a resource to distinguish orthogonal product states.

Zhi-Chao Zhang,Qiao-Yan Wen,Su-Juan Qin,Tian-Qing Cao,Fei Gao

doi:10.1038/srep30493

Abstract

It is known that there are many sets of orthogonal product states which cannot be distinguished perfectly by local operations and classical communication (LOCC). However, these discussions have left the following open question: What entanglement resources are necessary and/or sufficient for this task to be possible with LOCC? In m ⊗ n, certain classes of unextendible product bases (UPB) which can be distinguished perfectly using entanglement as a resource, had been presented in 2008. In this paper, we present protocols which use entanglement more efficiently than teleportation to distinguish some classes of orthogonal product states in m ⊗ n, which are not UPB. For the open question, our results offer rather general insight into why entanglement is useful for such tasks, and present a better understanding of the relationship between entanglement and nonlocality.

Highlights

In quantum information theory, one of the main goals is to understand the power and limitation of quantum operations which can be implemented by local operations and classical communication (LOCC)[1,2,3]
Our results show that the locally indistinguishable quantum states may become distinguishable with a small amount of entanglement resources
We present that a set of locally indistinguishable orthogonal product states in 5 ⊗ 5, can be perfectly distinguished by LOCC with a 2 ⊗ 2 maximally entangled state

Summary

Introduction

One of the main goals is to understand the power and limitation of quantum operations which can be implemented by local operations and classical communication (LOCC)[1,2,3]. We will consider the locally indistinguishable orthogonal product states in the general bipartite quantum systems and present the LOCC protocols which, using entanglement as a resource, distinguish these states considerably more efficiently than teleportation. In 5 ⊗ 5, we show a set of locally indistinguishable orthogonal product states can be distinguished by LOCC with a 2 ⊗ 2 maximally entangled state.

Results

Conclusion