N-Qubit W States are Determined by their Bipartite Marginals

TL;DR

This paper proves that the entire class of N-qubit W states can be uniquely identified using only their bipartite reduced density matrices, with fewer marginals needed for pure states.

Contribution

It establishes that W states are uniquely determined by bipartite marginals, reducing the number of necessary measurements for pure states to N-1.

Findings

W states are uniquely determined by bipartite marginals

Pure W states require only N-1 bipartite marginals for identification

The result applies to both pure and mixed states

Abstract

We prove that the most general W class of N-qubit states are uniquely determined among arbitrary states (pure or mixed) by just their bipartite reduced density matrices. Moreover, if we consider only pure states, then (N-1) of them are shown to be sufficient.