Symmetric Resourceful Steady States via Non-Markovian Dissipation

TL;DR

This paper proves a no-go theorem for symmetric steady states in Markovian spin systems and demonstrates that non-Markovian baths can generate unique, entangled steady states with specific symmetries, useful for quantum metrology.

Contribution

It establishes a no-go theorem for symmetric steady states in Markovian dynamics and shows how non-Markovian baths enable the creation of unique entangled steady states with desired symmetries.

Findings

Markovian spin systems cannot have unique symmetric steady states other than the maximally mixed state.

Non-Markovian baths can produce unique, entangled steady states with prescribed symmetries.

The framework is robust against microscopic bath details.

Abstract

We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states: in spin-only Lindblad dynamics with jump operators linear in the collective-spin operators, any unique steady state exhibiting at least $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry is necessarily the maximally mixed state. We then show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain, and providing a steady-state witness of non-Markovianity. Notably, this framework is largely insensitive to the microscopic details of the bath.