Scalability of GHZ and random-state entanglement in the presence of decoherence

TL;DR

This paper derives analytical bounds on the entanglement decay of GHZ and random states under decoherence, revealing exponential decay and discrepancies for random states that grow with system size.

Contribution

It provides tight analytical bounds for entanglement decay in GHZ states under various decoherence models and highlights differences with random states.

Findings

Entanglement decays exponentially with the number of particles.

Bounds are tight for depolarizing and dephasing channels.

Random states often violate these bounds, especially as system size increases.

Abstract

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.