Symmetric Resourceful Steady States via Non-Markovian Dissipation

• URL: http://arxiv.org/abs/2603.20091v1
• Date: Fri, 20 Mar 2026 16:15:18 GMT
• Title: Symmetric Resourceful Steady States via Non-Markovian Dissipation
• Abstract summary: We prove a no-go theorem for symmetry-based dissipative engineering of collective-spin steady states.<n>We show that bath memory lifts this obstruction, enabling unique entangled steady states with a prescribed symmetry and a metrological gain.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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