Theory of Ergodic Quantum Processes

The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity inclu...

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Autores principales:	Ramis Movassagh, Jeffrey Schenker
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/3b6c541883cb4be4b2216b15bf7188aa
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spelling	oai:doaj.org-article:3b6c541883cb4be4b2216b15bf7188aa2021-12-02T19:12:57ZTheory of Ergodic Quantum Processes10.1103/PhysRevX.11.0410012160-3308https://doaj.org/article/3b6c541883cb4be4b2216b15bf7188aa2021-10-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.041001http://doi.org/10.1103/PhysRevX.11.041001https://doaj.org/toc/2160-3308The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a replacement (rank-one) channel. Using this theorem, we derive the limiting behavior of translation-invariant channels and stochastically independent random channels. We then use our formalism to describe the thermodynamic limit of ergodic matrix product states. We derive formulas for the expectation value of a local observable and prove that the two-point correlations of local observables decay exponentially. We then analytically compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy (i.e., Rényi or von Neumann) across an arbitrary cut can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned. To obtain these results, we bridge quantum information theory to dynamical systems and random matrix theory.Ramis MovassaghJeffrey SchenkerAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 4, p 041001 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Ramis Movassagh Jeffrey Schenker Theory of Ergodic Quantum Processes
description	The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a replacement (rank-one) channel. Using this theorem, we derive the limiting behavior of translation-invariant channels and stochastically independent random channels. We then use our formalism to describe the thermodynamic limit of ergodic matrix product states. We derive formulas for the expectation value of a local observable and prove that the two-point correlations of local observables decay exponentially. We then analytically compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy (i.e., Rényi or von Neumann) across an arbitrary cut can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned. To obtain these results, we bridge quantum information theory to dynamical systems and random matrix theory.
format	article
author	Ramis Movassagh Jeffrey Schenker
author_facet	Ramis Movassagh Jeffrey Schenker
author_sort	Ramis Movassagh
title	Theory of Ergodic Quantum Processes
title_short	Theory of Ergodic Quantum Processes
title_full	Theory of Ergodic Quantum Processes
title_fullStr	Theory of Ergodic Quantum Processes
title_full_unstemmed	Theory of Ergodic Quantum Processes
title_sort	theory of ergodic quantum processes
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/3b6c541883cb4be4b2216b15bf7188aa
work_keys_str_mv	AT ramismovassagh theoryofergodicquantumprocesses AT jeffreyschenker theoryofergodicquantumprocesses
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Theory of Ergodic Quantum Processes

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