On small set of one-way LOCC indistinguishability of maximally entangled states

Abstract

In this paper, we study the one-way local operations and classical communication (LOCC) problem. In ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ with $d\ge 4$, we construct a set of $3\lceil \sqrt{d}\rceil -1$ one-way LOCC indistinguishable maximally entangled states which are generalized Bell states. Moreover, we show that there are four maximally entangled states which cannot be perfectly distinguished by one-way LOCC measurements for any dimension $d\ge 4$.

10 pages.Very recently, we became aware of related work \cite{Zhang2} in which the same $\lceil \frac{d}{2}\rceil +2$ states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ is proved to be one-way LOCC indistinguishable. arXiv admin note: text overlap with arXiv:1310.4220 by other author

References in corpus (2)

• Detecting the local indistinguishability of maximally entangled states
• $d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$

Cited by in corpus (9)

• Difficulty of distinguishing product states locally
• The local distinguishability of any three generalized Bell states
• Finding out all locally indistinguishable sets of generalized Bell states
• Local distinguishability of quantum states in multipartite System
• Detectors for local discrimination of sets of generalized Bell states
• The Independence of Distinguishability and the Dimension of the System
• Local unitary classification of sets of generalized Bell states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$
• Operator and Graph Theoretic Techniques for Distinguishing Quantum States via One-Way LOCC
• One-Way LOCC Indistinguishable Lattice States via Operator Structures