Local Equivalence of Rank-Two Quantum Mixed States

TL;DR

This paper establishes a complete set of invariants to determine when two rank-two quantum mixed states are equivalent under local unitary transformations, advancing understanding of quantum state classification.

Contribution

It provides a necessary and sufficient condition for local equivalence of rank-two mixed states using a complete set of invariants.

Findings

Identified a complete set of invariants for rank-two mixed states

Derived necessary and sufficient conditions for local equivalence

Enhanced classification methods for quantum mixed states

Abstract

We investigate the equivalence of quantum mixed states under local unitary transformations. For a class of rank-two mixed states, a sufficient and necessary condition of local equivalence is obtained by giving a complete set of invariants under local unitary transformations, such that two states in this class are locally equivalent if and only if all these invariants have equal values for them.