Four Locally Indistinguishable Ququad-Ququad Orthogonal Maximally Entangled States

TL;DR

This paper presents a set of four maximally entangled states in a 4x4 system that cannot be distinguished locally, introduces the concept of entanglement discrimination catalysis, and explores implications for quantum channel capacities.

Contribution

It explicitly constructs a set of four locally indistinguishable maximally entangled states and demonstrates entanglement discrimination catalysis, a novel phenomenon in quantum information.

Findings

Explicit example of four locally indistinguishable maximally entangled states

Introduction of entanglement discrimination catalysis

Construction of a quantum channel with full input dimension capacity

Abstract

We explicitly exhibit a set of four ququad-ququad orthogonal maximally entangled states that cannot be perfectly distinguished by means of local operations and classical communication. Before our work, it was unknown whether there is a set of $d$ locally indistinguishable $d\otimes d$ orthogonal maximally entangled states for some positive integer $d$. We further show that a $2\otimes 2$ maximally entangled state can be used to locally distinguish this set of states without being consumed, thus demonstrate a novel phenomenon of "Entanglement Discrimination Catalysis". Based on this set of states, we construct a new set $\mathrm{K}$ consisting of four locally indistinguishable states such that $\mathrm{K}^{\otimes m}$ (with $4^m$ members) is locally distinguishable for some $m$ greater than one. As an immediate application, we construct a noisy quantum channel with one sender and two receivers whose local zero-error classical capacity can achieve the full dimension of the input space but only with a multi-shot protocol.