Symmetry Properties of Quantum Dynamical Entropy

• URL: http://arxiv.org/abs/2502.04442v2
• Date: Thu, 13 Mar 2025 21:59:28 GMT
• Title: Symmetry Properties of Quantum Dynamical Entropy
• Authors: Eric D. Schultz, Keiichiro Furuya, Laimei Nie,
• Abstract summary: We study the precise behavior of quantum dynamical entropy in the presence of symmetry.<n>Our results highlight the role of symmetry in quantum dynamics under measurements.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: As quantum analogs of the classical Kolmogorov-Sinai entropy, quantum dynamical entropies have emerged as important tools to characterize complex quantum dynamics. In particular, Alicki-Fannes-Lindblad (AFL) entropy, which quantifies the information production of a coherent quantum system subjected to repeated measurement, has received considerable attention as a potential diagnostic for quantum chaos. Despite this interest, the precise behavior of quantum dynamical entropy in the presence of symmetry has seen little study. In this work, we establish rigorous inequalities of the AFL entropy for arbitrary unitary dynamics (single-particle and many-body) in the presence of various types of symmetry. Our theorems encompass three cases: Abelian symmetry, an anticommuting unitary, and non-Abelian symmetries. We motivate our main results with numerical simulations of the perturbed quantum cat maps. Our findings highlight the role of symmetry in quantum dynamics under measurements, and our framework is easily adaptable for study of symmetry in other probes of quantum chaos.

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