Identifying the $3$-qubit $W$ state with quantum uncertainty relation

TL;DR

This paper presents a new method using quantum uncertainty relations to efficiently identify tripartite W states without full state tomography, enhancing entanglement characterization.

Contribution

It introduces an uncertainty-based criterion for distinguishing W states from other tripartite entangled states, bypassing the need for complete quantum state tomography.

Findings

The method effectively identifies W states using uncertainty inequalities.

It distinguishes W states from GHZ states.

The approach simplifies entanglement detection in multipartite systems.

Abstract

The $W$ state, a canonical representative of multipartite quantum entanglement, plays a crucial role in quantum information science due to its robust entanglement properties. Quantum uncertainty relations, on the other hand, are a fundamental cornerstone of quantum mechanics. This paper introduces a novel approach to Identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations. By employing a specific set of non-commuting observables, we formulate an uncertainty-based criterion for identifying $W$ states and rigorously demonstrate its generality in distinguishing them from other tripartite entangled states, such as the Greenberger-Horne-Zeilinger state. Our approach bypasses the need for complete quantum state tomography, as it requires only the verification of a set of uncertainty inequalities for efficient $W$-state identification. This work provides a new theoretical tool for identifying multipartite entangled states and underscores the significant role of quantum uncertainty relations in entanglement characterization.