Entanglement Sudden Death: Eberly's Work and the Limits of Local Dynamics

Abstract

Entanglement sudden death (ESD), explored through a series of works by Yu and Eberly, supports the notion of entanglement vanishing abruptly and completely at a finite time, even when the underlying open-system dynamics remain smooth. In this article, we revisit the development of ESD from bipartite origins to genuine multipartite entanglement. We first illustrate the canonical mechanism of ESD with two independently damped qubits, for which the concurrence vanishes at a finite time while populations and coherences remain nonzero. We next present our results on multipartite entanglement for generalized GHZ states under depolarization. Global and independent local depolarizing dynamics can be chosen to produce identical reduced evolution for every individual qubit, yet they yield different genuine-multipartite-entanglement sudden death times, whose ordering can reverse with the initial state. For N-qubit GHZ states, this distinction becomes asymptotically stronger since the ESD time scales as 1/N under independent local depolarization, whereas under global depolarization it approaches a finite value in the thermodynamic limit. Echoing a central lesson of Prof. Eberly's work, we report the lifetime of multipartite entanglement is not fixed by the local dynamics, but rather depends on the evolution of the joint quantum state.