Dynamical entanglement percolation with spatially correlated disorder

TL;DR

This paper explores how entanglement propagates in quantum networks with spatially correlated disorder, revealing complex percolation behavior influenced by unitary dynamics and disorder correlations.

Contribution

It introduces a two-colour correlated bond percolation model and combines numerical simulations with mean-field theory to analyze entanglement dynamics in disordered quantum networks.

Findings

Disorder correlations induce non-standard percolation phenomena.

Hysteresis appears in the entanglement percolation process.

The phase diagram is characterized by numerical and mean-field methods.

Abstract

The distribution of entanglement between the nodes of a quantum network plays a fundamental role in quantum information applications. In this work, we investigate the dynamics of a network of qubits where each edge corresponds to an independent two-qubit interaction. By applying tools from percolation theory, we study how entanglement dynamically spreads across the network. We show that the interplay between unitary evolution and spatially correlated disorder leads to a non-standard percolation phenomenology, significantly richer than uniform bond percolation and featuring hysteresis. A two-colour correlated bond percolation model, whose phase diagram is determined via numerical simulations and a mean-field theory, fully elucidates the physics behind this phenomenon.