Multi-partite $W-$type state is determined by its single particle reduced density matrices

TL;DR

This paper proves that multi-partite W-type quantum states can be uniquely identified by their single-particle reduced density matrices, up to local unitary transformations.

Contribution

It establishes a uniqueness result for W-type states based solely on single-particle reduced density matrices, advancing understanding of quantum state determination.

Findings

W-type states are uniquely determined by single-particle reductions

The result holds up to local unitary transformations

Provides insight into quantum state reconstruction

Abstract

In this short note, we show that multi-partite $W$-type state is up to local unitaries uniquely determined by its reduced density matrices.