Symmetric Resourceful Steady States via Non-Markovian Dissipation

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.

Source: arXiv:2603.20091v1 - http://arxiv.org/abs/2603.20091v1 PDF: https://arxiv.org/pdf/2603.20091v1 Original Link: http://arxiv.org/abs/2603.20091v1