Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-11-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.14.041051 |
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| author | Daniel K. Mark Federica Surace Andreas Elben Adam L. Shaw Joonhee Choi Gil Refael Manuel Endres Soonwon Choi |
| author_facet | Daniel K. Mark Federica Surace Andreas Elben Adam L. Shaw Joonhee Choi Gil Refael Manuel Endres Soonwon Choi |
| author_sort | Daniel K. Mark |
| collection | DOAJ |
| description | We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools. |
| format | Article |
| id | doaj-art-f249257f712c405189d41a56c97be871 |
| institution | OA Journals |
| issn | 2160-3308 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj-art-f249257f712c405189d41a56c97be8712025-08-20T02:23:35ZengAmerican Physical SocietyPhysical Review X2160-33082024-11-0114404105110.1103/PhysRevX.14.041051Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space ErgodicityDaniel K. MarkFederica SuraceAndreas ElbenAdam L. ShawJoonhee ChoiGil RefaelManuel EndresSoonwon ChoiWe report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by (i) the temporal trajectory of a quantum state under unitary evolution or (ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases, respectively, exemplify the phenomena of “Hilbert-space ergodicity” and “deep thermalization.” In both cases, the resultant ensembles are defined by a simple principle: The distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulas for all statistical moments of the ensembles, proving the necessary and sufficient conditions for such universality under widely accepted assumptions, and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: Our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information-theoretic tools.http://doi.org/10.1103/PhysRevX.14.041051 |
| spellingShingle | Daniel K. Mark Federica Surace Andreas Elben Adam L. Shaw Joonhee Choi Gil Refael Manuel Endres Soonwon Choi Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity Physical Review X |
| title | Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity |
| title_full | Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity |
| title_fullStr | Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity |
| title_full_unstemmed | Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity |
| title_short | Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity |
| title_sort | maximum entropy principle in deep thermalization and in hilbert space ergodicity |
| url | http://doi.org/10.1103/PhysRevX.14.041051 |
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