Typical behaviour of the global entanglement of an open multiqubit system in a non-markovian regimen

TL;DR

This paper studies how global entanglement in multiqubit systems decays under non-Markovian decoherence, using numerical simulations of random initial states and specific important states across systems of 3 to 6 qubits.

Contribution

It provides a numerical analysis of the average entanglement decay for random initial states in multiqubit systems under non-Markovian decoherence, extending beyond special initial states.

Findings

Average entanglement decay patterns identified for 3-6 qubits.

GHZ and maximally entangled states often represent typical behavior.

Non-Markovian effects influence entanglement dynamics significantly.

Abstract

We investigate the decay of the global entanglement, due to decoherence, of multiqubit systems interacting with a reservoir in a non Markovian regime. We assume that during the decoherence process each qubit of the system interacts with its own, independent environment. Most previous works on this problem focused on particular initial states or families of initial states amenable of analytical treatment. Here we determine numerically the typical, average behaviour of the system corresponding to random initial pure states uniformly distributed (in the whole Hilbert space of $n$-qubit pure states) according to the Haar measure. We study systems consisting of 3, 4, 5, and 6 qubits. In each case we consider also the entanglement dynamics corresponding to important particular initial states, such as the GHZ states or multiqubit states maximizing the global entanglement, and determine in which cases any of these states is representative of the average behaviour associated with general initial states.