Absence of Correlations in Dissipative Interacting Qubits: a No-Go Theorem

TL;DR

This paper proves a no-go theorem showing that dissipative qubits with certain conditions cannot develop correlations, impacting quantum synchronization and enabling network simplification, with proposed experimental tests.

Contribution

It presents an exact steady state solution and a no-go theorem for correlations in dissipative qubits, revealing new limits on quantum synchronization.

Findings

Correlations cannot form between qubits with identical damping/gain ratios.

Quantum synchronization is completely blocked under the theorem's conditions.

Complex qubit networks can be simplified through engineered dissipation.

Abstract

Exact solutions of model problems are elusive but potent tools for understanding many body interacting systems. We study a system of dissipative qubits with the Heisenberg interaction and obtain, for qubits under a certain condition, an exact steady state solution to the Lindblad master equation describing its dynamics. The physical content of such a solution is a remarkable no-go theorem, which states that for qubits possessing identical ratios of the damping and gain rates, no correlation can be established between them in the steady state. Two consequences of this theorem are discussed in the context of quantum synchronization of qubits. The first is a complete blockade of quantum synchronization of qubits under the aforementioned condition, an effect reminiscent of, but having a much broader scope than, that found in dissipated Kerr-anharmonic oscillators. The second, and a more important consequence is the possibility of reducing a complex all-to-all qubit network to a much simpler one-to-all network by engineering the dissipation. Such a reduction is desired because it provides an effective tool to optimize the quantum synchronization of a complex qubit network. Finally, we propose two concrete experimental schemes to implement our model and to test our predictions.