Universal spectra of random Lindblad operators

Abstract

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

6 pages, 4 figures + supplemental material

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• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• From integrability to chaos in quantum Liouvillians
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
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• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
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• Probing quantum chaos in multipartite systems
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• Efficient flow equations for dissipative systems
• Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of $SU(N)$ generators
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• Universal Time-Entanglement Trade-off in Open Quantum Systems
• Higher-order gap ratios of singular values in open quantum systems
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• Ringdown in the SYK model
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• Localization of Lindbladian Fermions
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• Nonlinear unitary circuits for photonic neural networks
• Dissipative chaos and steady state of open Tavis-Cummings dimer
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