Local unitary equivalence of multipartite pure states

TL;DR

This paper establishes necessary and sufficient conditions for determining when multipartite pure quantum states are equivalent under local unitary operations, introducing a standard form and systematic methods for both generic and non-generic states.

Contribution

It provides a comprehensive framework for checking local unitary equivalence of multipartite pure states, including a standard form and a method for non-generic cases.

Findings

Standard form for multipartite states introduced

LU-equivalence iff standard forms coincide

Systematic method for non-generic states developed

Abstract

Necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations are derived. First, an easily computable standard form for multipartite states is introduced. Two generic states are shown to be LU-equivalent iff their standard forms coincide. The LU-equivalence problem for non--generic states is solved by presenting a systematic method to determine the LU operators (if they exist) which interconvert the two states.