Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations

TL;DR

This paper introduces a geometric framework to determine when bipartite quantum mixed states are equivalent under local unitary transformations, providing a new method for classifying quantum states.

Contribution

It proposes the concept of representation classes from a geometrical perspective to identify equivalence of bipartite quantum states under local unitaries, with practical calculation examples.

Findings

Representation classes uniquely characterize state equivalence.

Two states are equivalent iff they share the same representation class.

Method simplifies classification of bipartite quantum states.

Abstract

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes.