On Local Unitary Equivalence of Two and Three-qubit States

TL;DR

This paper investigates the criteria for local unitary equivalence of two and three-qubit mixed states by constructing and analyzing invariants, providing a more efficient method for determining state equivalence.

Contribution

It introduces a minimal set of invariants for two-qubit states and constructs invariants for three-qubit states, advancing the understanding of LU equivalence.

Findings

14 or fewer invariants suffice for two-qubit state equivalence

Constructed invariants for three-qubit states that guarantee LU equivalence in certain cases

Compared new invariants with earlier methods to demonstrate improvements

Abstract

We study the local unitary equivalence for two and three-qubit mixed states by investigating the invariants under local unitary transformations. For two-qubit system, we prove that the determination of the local unitary equivalence of 2-qubits states only needs 14 or less invariants for arbitrary two-qubit states. Using the same method, we construct invariants for three-qubit mixed states. We prove that these invariants are sufficient to guarantee the LU equivalence of certain kind of three-qubit states. Also, we make a comparison with earlier works.