Scaling laws for the decay of multiqubit entanglement

TL;DR

This paper derives scaling laws for how multiqubit GHZ state entanglement decays and experiences sudden death in independent reservoirs, revealing that entanglement becomes useless well before complete disappearance and can generate bound entangled states.

Contribution

It introduces new scaling laws for entanglement decay and sudden death times in multiqubit GHZ states interacting with reservoirs.

Findings

Entanglement decay time scales inversely with the number of particles.

Entanglement becomes negligible before complete decay.

Decay can lead to the formation of bound entangled states.

Abstract

We investigate the decay of entanglement of generalized N-particle Greenberger-Horne-Zeilinger (GHZ) states interacting with independent reservoirs. Scaling laws for the decay of entanglement and for its finite-time extinction (sudden death) are derived for different types of reservoirs. The latter is found to increase with the number of particles. However, entanglement becomes arbitrarily small, and therefore useless as a resource, much before it completely disappears, around a time which is inversely proportional to the number of particles. We also show that the decay of multi-particle GHZ states can generate bound entangled states.