Mixing properties of stochastic quantum hamiltonians

E. Onorati , O. Buerschaper , Martin Kliesch , W. Brown , A. H. Werner , J. Eisert

Abstract

Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and quantum information theory. In this work, we present a framework describing the mixing properties of continuous-time unitary evolutions originating from local Hamiltonians having time-fluctuating terms, reflecting a Brownian motion on the unitary group. The induced stochastic time evolution is shown to converge to a unitary design. As a first main result, we present bounds to the mixing time. By developing tools in representation theory, we analytically derive an expression for a local k-th moment operator that is entirely independent of k, giving rise to approximate unitary k-designs and quantum tensor product expanders. As a second main result, we introduce tools for proving bounds on the rate of decoupling from an environment with random quantum processes. By tying the mathematical description closely with the more established one of random quantum circuits, we present a unified picture for analysing local random quantum and classes of Markovian dissipative processes, for which we also discuss applications.
Author E. Onorati
E. Onorati,,
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, O. Buerschaper
O. Buerschaper,,
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, Martin Kliesch IFTiA
Martin Kliesch,,
- Institute of Theoretical Physics and Astrophysics
, W. Brown
W. Brown,,
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, A. H. Werner
A. H. Werner,,
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, J. Eisert
J. Eisert,,
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Other language title versions
Journal seriesCommunications in Mathematical Physics, ISSN 0010-3616
Issue year2017
Vol355
No3
Pages905-947
Publication size in sheets2.1
DOIDOI:10.1007/s00220-017-2950-6
URL https://link.springer.com/content/pdf/10.1007%2Fs00220-017-2950-6.pdf
Languageen angielski
Score (nominal)40
ScoreMinisterial score = 40.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 2.5 (2) - 2016=2.38 (5)
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