Entanglement of Assistance as a measure of multiparty entanglement

TL;DR

This paper introduces the Volume of Assistance (VoA), a novel geometric mean-based measure for quantifying multipartite entanglement, demonstrating its applicability, advantages over existing measures, and practical utility in quantum models.

Contribution

The paper proposes VoA, extending it to multipartite states, and compares it with existing measures, showing its effectiveness in distinguishing complex entangled states.

Findings

VoA is feasible for three-qubit pure states and some qudit states.

VoA serves as an upper bound for the generalized geometric measure.

VoA effectively distinguishes states that MPC cannot differentiate.

Abstract

Quantifying multipartite entanglement poses a significant challenge in quantum information theory, prompting recent advancements in methodologies to assess it. We introduce the notion of \enquote{Volume of Assistance} (VoA), which computes the geometric mean of entanglement of assistance across all potential parties. We demonstrate the feasibility of VoA for three-qubit pure states and certain classes of pure tripartite qudit states. We have extended this measure to four-qubit states and general multipartite scenarios. We have done a comparative analysis to illustrate VoA's distinctiveness from established entanglement measures, notably showing it serves as an upper bound for the much celebrated generalized geometric measure (GGM). Remarkably, VoA excels in distinguishing a broad class of states that elude differentiation by the recently proposed Minimum Pairwise Concurrence (MPC) measure. Finally, VoA is applied to quantify genuine entanglement in the ground states of a three-qubit Heisenberg XY model, which highlights its practical utility in quantum information processing tasks.