A Complete Set of Local Invariants for a Family of Multipartite Mixed States

TL;DR

This paper introduces a comprehensive set of invariants based on singular value decomposition to determine when multipartite mixed quantum states are equivalent under local unitary transformations, aiding quantum state classification.

Contribution

It presents a complete set of local invariants for certain tripartite mixed states, enabling precise classification under local unitary equivalence.

Findings

Invariants successfully distinguish equivalent states.

Complete invariants for specific tripartite classes.

Method based on singular value decomposition.

Abstract

We study the equivalence of quantum states under local unitary transformations by using the singular value decomposition. A complete set of invariants under local unitary transformations is presented for several classes of tripartite mixed states in KxMxN composite systems. Two density matrices in the same class are equivalent under local unitary transformations if and only if all these invariants have equal values for these density matrices.