Symmetric Resourceful Steady States via Non-Markovian Dissipation

Quantum Physics [Submitted on 20 Mar 2026] Symmetric Resourceful Steady States via Non-Markovian Dissipation Baptiste Debecker, Eduardo Serrano-Ensástiga, Thierry Bastin, François Damanet, John Martin 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. Comments: 5 pages and 4 figures (main); 6 pages and 1 figure (supplemental) Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20091 [quant-ph]   (or arXiv:2603.20091v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20091 Focus to learn more Submission history From: Baptiste Debecker [view email] [v1] Fri, 20 Mar 2026 16:15:18 UTC (9,099 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)