Unified Construction of Genuine Multipartite Entanglement Measures Based on Geometric Mean and its Applications

TL;DR

This paper introduces a unified framework for constructing genuine multipartite entanglement measures using geometric means, providing analytical bounds and analyzing their dynamics in complex quantum systems.

Contribution

It presents a systematic method to unify various GME measures based on geometric means, with tight bounds and applications to quantum dynamics.

Findings

Derived tight, experiment-friendly lower bounds for GME measures.

Analyzed the impact of initial conditions on entanglement sudden death.

Studied GME behavior of Dirac particles near black holes.

Abstract

Genuine multipartite entanglement (GME) is an important resource in quantum information processing. We systematically study the measures of GME based on the geometric mean of bi-partition entanglements and present a unified construction of GME measures, which gives rise to the widely used GME measures including GME concurrence, the convex-roof extended negativity of GME, the geometric measure of entanglement of GME. Our GME measures satisfy the desirable conditions such as scalability and smoothness. Moreover, we provide fidelity-based analytical lower bounds for our GME measures. Our bounds are tight and can be estimated experiment friendly without requiring quantum state tomography. Furthermore, we apply our results to study the dynamics of GME. We identify an initial condition that influences the sudden death of genuine quadripartite entanglement under individual non-Markovian processes. The GME of Dirac particles with Hawking radiation in the background of a Schwarzschild black hole is also investigated.