Entanglement assisted state discrimination and entanglement preservation

TL;DR

This paper explores how pre-shared entanglement enables two distant parties to perfectly distinguish among four orthogonal entangled states of qubits and preserve their entanglement after discrimination, using majorization theory.

Contribution

It demonstrates that pre-shared entanglement can be used to achieve perfect discrimination and entanglement preservation for four orthogonal entangled states, extending understanding of entanglement-assisted protocols.

Findings

Pre-shared entanglement enables perfect discrimination of four orthogonal states.

The protocol preserves entanglement after state discrimination.

Majorization theory links entanglement transformations to discrimination capabilities.

Abstract

In this paper, the following scenario is considered: there are two qubits possessed by two parties at different locations. Qubits have been prepared in one of a maximum of four, mutually-orthogonal, entangled states and the parties wish to distinguish between the states by using local operations and classical communication. Although in general it is not possible to distinguish between four arbitrary states, the parties can spend some pre-shared entanglement to achieve perfect discrimination between four qubit states and can also preserve the entanglement of the states after discrimination. This is shown by employing the theory of majorization and the connections between entanglement transformations and state discrimination protocols.