Local unitary equivalent consistence for n-party states and their (n-1)-party reduced density matrices

TL;DR

This paper demonstrates that the local unitary equivalence of n-party pure states aligns with that of their (n-1)-party reduced density matrices, providing a method to derive local invariants for tripartite pure qudits.

Contribution

It establishes the consistency between local unitary equivalence of n-party states and their (n-1)-party reduced states, and derives local invariants for tripartite pure qudits.

Findings

Local unitary equivalence is consistent between n-party states and their (n-1)-party reductions.

Derived local invariants for a class of tripartite pure qudits.

Provides a new approach to analyze multipartite quantum states.

Abstract

We present that the local unitary equivalence of n-party pure states is consistent with the one of their (n-1)-party reduced density matrices. As an application, we obtain the local invariants for a class of tripartite pure qudits.