Local Unitary Equivalence of Multi-qubit Mixed quantum States

TL;DR

This paper introduces a practical criterion for classifying multi-qubit mixed quantum states under local unitary transformations, enabling both theoretical classification and experimental verification.

Contribution

It provides a computable and observable-based method to determine local unitary equivalence and explicitly compute the associated unitary operators.

Findings

The criterion is fully computable for multi-qubit states.

It allows experimental detection of local unitary equivalence.

The method can explicitly find the unitary operators when states are equivalent.

Abstract

We present computable criterion for completely classifying multi-qubit quantum states under local unitary operations. The criterion can be used to detect whether two quantum states in multi-qubit systems are local unitary equivalent or not. Once obtaining the positive answer, we are further able to compute the corresponding unitary operators precisely. Since the scheme is based on the mean values of some quantum mechanical observables, it supplies an experimental way to judge the local equivalence of quantum states.