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Spectral transitions and universal steady states in random Kraus maps and circuits
- Source :
- Physical Review B
- Publication Year :
- 2020
- Publisher :
- American Physical Society (APS), 2020.
-
Abstract
- The study of dissipation and decoherence in generic open quantum systems recently led to the investigation of spectral and steady-state properties of random Lindbladian dynamics. A natural question is then how realistic and universal those properties are. Here, we address these issues by considering a different description of dissipative quantum systems, namely, the discrete-time Kraus map representation of completely positive quantum dynamics. Through random matrix theory (RMT) techniques and numerical exact diagonalization, we study random Kraus maps, allowing for a varying dissipation strength, and their local circuit counterpart. We find the spectrum of the random Kraus map to be either an annulus or a disk inside the unit circle in the complex plane, with a transition between the two cases taking place at a critical value of dissipation strength. The eigenvalue distribution and the spectral transition are well described by a simplified RMT model that we can solve exactly in the thermodynamic limit, by means of non-Hermitian RMT and quaternionic free probability. The steady state, on the contrary, is not affected by the spectral transition. It has, however, a perturbative crossover regime at small dissipation, inside which the steady state is characterized by uncorrelated eigenvalues. At large dissipation (or for any dissipation for a large-enough system), the steady state is well described by a random Wishart matrix. The steady-state properties thus coincide with those already observed for random Lindbladian dynamics, indicating their universality. Quite remarkably, the statistical properties of the local Kraus circuit are qualitatively the same as those of the nonlocal Kraus map, indicating that the latter, which is more tractable, already captures the realistic and universal physical properties of generic open quantum systems.<br />15 pages, 8 figures. v2: additional details, version as published
- Subjects :
- Quantum decoherence
Quantum dynamics
FOS: Physical sciences
02 engineering and technology
01 natural sciences
0103 physical sciences
Statistical physics
010306 general physics
Quantum
Condensed Matter - Statistical Mechanics
Eigenvalues and eigenvectors
Physics
Quantum Physics
Statistical Mechanics (cond-mat.stat-mech)
Disordered Systems and Neural Networks (cond-mat.dis-nn)
Condensed Matter - Disordered Systems and Neural Networks
Dissipation
Nonlinear Sciences - Chaotic Dynamics
16. Peace & justice
021001 nanoscience & nanotechnology
Thermodynamic limit
Dissipative system
Chaotic Dynamics (nlin.CD)
Quantum Physics (quant-ph)
0210 nano-technology
Random matrix
Subjects
Details
- ISSN :
- 24699969 and 24699950
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Physical Review B
- Accession number :
- edsair.doi.dedup.....55f1f6ebacb67da6001936ea75ee088f