Stationary and uniform entanglement distribution in qubit networks with quasi-local dissipation

TL;DR

This paper demonstrates that in qubit networks with quasi-local dissipation, the steady states are symmetric, resulting in uniform entanglement distribution that scales linearly with the number of qubits, with potential physical realizations discussed.

Contribution

The paper provides exact solutions for steady states in qubit networks with quasi-local dissipation, revealing uniform entanglement distribution and its dependence on network size.

Findings

Steady states are symmetric under permutation of sites.

Stationary entanglement distribution is uniform across the network.

Maximum pairwise entanglement scales linearly with total qubits.

Abstract

We consider qubit networks where adjacent qubits besides interacting via XY-coupling, also dissipate into the same environment. The steady states are computed exactly for all network sizes and topologies, showing that they are always symmetric under permutation of network sites, leading to a uniform distribution of the stationary entanglement across the network. The maximum entanglement between two arbitrary qubits is shown to depend only on the total number of qubits in the network, and scales linearly with it. A possible physical realization by means of an array of doped cavities is discussed for the case of a linear chain.