Universal Spectra of Random Lindblad Operators

Sergey Denisov, Tetyana Laptyeva, Wojciech Tarnowski, Dariusz Chruściński, and Karol Życzkowski
Phys. Rev. Lett. 123, 140403 – Published 1 October 2019
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Abstract

To understand the typical dynamics of an open quantum system in continuous time, we introduce an ensemble of random Lindblad operators, which generate completely positive Markovian evolution in the space of the density matrices. The spectral properties of these operators, including the shape of the eigenvalue distribution in the complex plane, are evaluated by using methods of free probabilities and explained with non-Hermitian random matrix models. We also demonstrate the universality of the spectral features. The notion of an ensemble of random generators of Markovian quantum evolution constitutes a step towards categorization of dissipative quantum chaos.

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  • Received 4 December 2018
  • Corrected 4 October 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.140403

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyGeneral PhysicsStatistical Physics & Thermodynamics

Corrections

4 October 2019

Correction: An incorrect affiliation for the fourth author was processed and has been fixed.

Authors & Affiliations

Sergey Denisov1,2, Tetyana Laptyeva2, Wojciech Tarnowski3, Dariusz Chruściński4, and Karol Życzkowski3,5

  • 1Department of Computer Science, OsloMet–Oslo Metropolitan University, NO-0130 Oslo, Norway
  • 2Department of Control Theory and Systems Dynamics, Lobachevsky University, Gagarina Avenue 23, Nizhny Novgorod, 603950, Russia
  • 3Marian Smoluchowski Institute of Physics, Uniwersytet Jagielloński, Krakow, Poland
  • 4Institute of Physics, Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University, Grudziadzka 5/7, 87–100 Torun, Poland
  • 5Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warszawa, Poland

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Issue

Vol. 123, Iss. 14 — 4 October 2019

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