Quantum i.i.d. Steady States in Open Many-Body Systems

• URL: http://arxiv.org/abs/2507.10319v1
• Date: Mon, 14 Jul 2025 14:28:39 GMT
• Title: Quantum i.i.d. Steady States in Open Many-Body Systems
• Authors: Takanao Ishii, Masahito Ueda,
• Abstract summary: We establish a general equivalent condition for an open quantum many-body system governed by the Gorini-Kossakowski-Sudarshan-Lindblad dynamics.<n>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.
• Score: 9.361474110798143
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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