Local unitary equivalence and entanglement of multipartite pure states

TL;DR

This paper classifies the local unitary equivalence classes of up to five-qubit pure states, introduces new entanglement parameters, and demonstrates states with identical subsystem entropies that are not LU-equivalent.

Contribution

It extends the classification of multipartite entanglement by deriving new parameters and analyzing states with identical entropies but different LU classes.

Findings

Classified LU-equivalence for up to five-qubit states

Identified new parameters characterizing multipartite entanglement

Found states with identical subsystem entropies that are not LU-equivalent

Abstract

The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two n-qubit states (with n>2 arbitrary) which have the properties that all the entropies of any subsystem coincide, however, the states are neither LU-equivalent nor can be mapped into each other by general local operations and classical communication.