Quantum i.i.d. Steady States in Open Many-Body Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916920187420672 |
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| author | Ishii, Takanao Ueda, Masahito |
| author_facet | Ishii, Takanao Ueda, Masahito |
| contents | Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent condition for an open quantum many-body system governed by the Gorini-Kossakowski-Sudarshan-Lindblad dynamics under local drive and/or dissipation to have a quantum independent and identically distributed (i.i.d.) steady state. We present a sufficient condition for a system to have a quantum i.i.d. steady state by identifying a set of operators that commute with arbitrary quantum i.i.d. states. In particular, a set of quantum i.i.d. states is found to be an invariant subset of time evolution superoperators for systems that satisfy the sufficient condition. These findings not only identify a class of models with exactly solvable steady states but also lead to a no-go theorem that precludes quantum entanglement and spatial correlations in a broad class of quantum many-body steady states in a dissipative environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10319 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum i.i.d. Steady States in Open Many-Body Systems Ishii, Takanao Ueda, Masahito Quantum Physics Statistical Mechanics Mathematical Physics Understanding how a quantum many-body state is maintained stably as a nonequilibrium steady state is of fundamental and practical importance for exploration and exploitation of open quantum systems. We establish a general equivalent condition for an open quantum many-body system governed by the Gorini-Kossakowski-Sudarshan-Lindblad dynamics under local drive and/or dissipation to have a quantum independent and identically distributed (i.i.d.) steady state. We present a sufficient condition for a system to have a quantum i.i.d. steady state by identifying a set of operators that commute with arbitrary quantum i.i.d. states. In particular, a set of quantum i.i.d. states is found to be an invariant subset of time evolution superoperators for systems that satisfy the sufficient condition. These findings not only identify a class of models with exactly solvable steady states but also lead to a no-go theorem that precludes quantum entanglement and spatial correlations in a broad class of quantum many-body steady states in a dissipative environment. |
| title | Quantum i.i.d. Steady States in Open Many-Body Systems |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2507.10319 |