Collective Uncertainty Entanglement Test

TL;DR

This paper introduces a new entanglement measure called collectibility, based on bounds of projections onto orthogonal separable states, aiding experimental quantification of entanglement and identifying genuine three-party entanglement.

Contribution

It derives a novel bound for product projections, constructs the collectibility measure, and demonstrates its effectiveness in quantifying and identifying multipartite entanglement.

Findings

Bound is saturated for maximally entangled bipartite states.

Collectibility can be experimentally measured.

Method identifies genuine three-party entanglement in three-qubit systems.

Abstract

For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.