Synchronization in a dissipative quantum many-body system

TL;DR

This paper investigates how synchronization and entanglement emerge in a dissipative quantum spin chain, revealing conditions under which stable synchronization and constant entanglement coexist or depend on initial states.

Contribution

It provides a complete characterization of the decoherence-free subspace structure and identifies precise conditions for stable synchronization and persistent entanglement in the system.

Findings

Stable synchronization occurs if and only if the DFS has exactly one single-excitation eigenstate.

Constant asymptotic entanglement between edge qubits is guaranteed under the same condition.

Synchronization can be absent or initial state dependent when multiple single-excitation eigenstates are supported.

Abstract

We study synchronization in the XX qubit chain subject to local or multi-local amplitude-damping noise. Analyzing the decoherence-free subspace (DFS) structure of the model, we show that it is completely determined by a simple number-theoretic function involving the noise sites and the chain length. We derive a closed-form expression for local qubit observables restricted to the DFS and prove that stable synchronization of the edge qubits for arbitrary initial states occurs \textit{if and only if} the DFS supports exactly one single-excitation eigenstate. We further show that this same condition also guarantees constant asymptotic entanglement between the edge qubits, so that generic stable synchronization and constant asymptotic entanglement necessarily coexist. By contrast, when the DFS supports multiple single-excitation eigenstates, synchronization becomes initial state dependent and may be entirely absent, even though stable oscillatory entanglement can persist indefinitely.