Criterion for SLOCC Equivalence of Multipartite Quantum States

TL;DR

This paper establishes a comprehensive criterion for determining SLOCC equivalence among multipartite quantum states, applicable to both pure and mixed states, facilitating classification based on matrix properties.

Contribution

It introduces necessary and sufficient conditions for SLOCC equivalence using coefficient matrix ranks for pure states and realignment for mixed states, advancing quantum state classification.

Findings

Criterion based on coefficient matrix rank for pure states

Realignment method for mixed state SLOCC equivalence

Examples demonstrating the classification process

Abstract

We study the stochastic local operation and classical communication (SLOCC) equivalence for arbitrary dimensional multipartite quantum states. For multipartite pure states, we present a necessary and sufficient criterion in terms of their coefficient matrices. This condition can be used to classify some SLOCC equivalent quantum states with coefficient matrices having the same rank. For multipartite mixed state, we provide a necessary and sufficient condition by means of the realignment of matrix. Some detailed examples are given to identify the SLOCC equivalence of multipartite quantum states.