A statistical portrait of the entanglement decay of two-qubit memories

TL;DR

This paper introduces a statistical approach to analyze how entanglement in two-qubit systems decays under various decoherence channels, providing analytical and numerical insights into disentanglement times and concurrence evolution.

Contribution

It presents a novel collective property-based method for studying entanglement decay, including analytical results for pure states and numerical analysis for mixed states, applicable to Markovian and non-Markovian channels.

Findings

Probability distributions of disentanglement times are independent of entanglement measure.

Analytical results are derived for initially uniformly distributed pure states.

Numerical results illustrate effects on mixed states under various decoherence channels.

Abstract

We present a novel approach to the study of entanglement decay, which focuses on collective properties. As an example, we investigate the entanglement decay of a two-qubit system, produced by local identical reservoirs acting on the qubits, for three experimentally and theoretically relevant cases. We study the probability distributions of disentanglement times, a quantity independent of the measure used to quantify entanglement, and the time-dependent probability distribution of concurrence. Analytical results are obtained for initially uniformly distributed pure states. The calculation of these probability distributions gives a complete insight on how different decoherence channels affect the entanglement initially contained in the set of two-qubit pure states. Numerical results are reported for randomly distributed initial mixed states. Although the paper focuses in Markovian noisy channels, we show that our results also describe non-autonomous and non-Markovian channels.