Ergodic repeated interaction quantum systems: Steady states and reducibility theory

• URL: http://arxiv.org/abs/2406.10982v1
• Date: Sun, 16 Jun 2024 15:38:20 GMT
• Title: Ergodic repeated interaction quantum systems: Steady states and reducibility theory
• Authors: Owen Ekblad, Jeffrey Schenker,
• Abstract summary: We consider the time evolution of an open quantum system subject to a sequence of random quantum channels with a stationary distribution. Various specific models of disorder in repeated interaction models have been considered. We develop a reducarity theory for general stationary random repeated interaction models without this condition.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the time evolution of an open quantum system subject to a sequence of random quantum channels with a stationary distribution. This incorporates disorder into the repeated interactions (or, quantum collision models) approach to understanding open quantum dynamics. In the literature, various specific models of disorder in repeated interaction models have been considered, including the cases where the sequence of quantum channels form either i.i.d. or Markovian stochastic processes. In the present paper we consider the general structure of such models without any specific assumptions on the probability distribution, aside from stationarity (i.e., time-translation invariance). In particular, arbitrarily strong correlations between time steps are allowed. In 2021, Movassagh and Schenker (MS) introduced a unified framework in which one may study such randomized quantum dynamics, and, under a key strong decoherence assumption proved an ergodic theorem for a large class of physically relevant examples. Here, we recognize the decoherence assumption of MS as a kind of irreducibility and develop a reducibility theory for general stationary random repeated interaction models without this condition. Within this framework, we establish ergodic theorems extending of those obtained by MS to the general stationary setting.

Related papers

• Compatibility of Quantum Measurements and the Emergence of Classical Objectivity [0.0]
  We consider the KDQ distributions describing arbitrary collections of measurements on disjoint components of some generic multipartite system. We show that the system dynamics ensures that these distributions are classical if and only if the Hamiltonian supports Quantum Darwinism.
  arXiv  Detail & Related papers  (2024-11-16T19:01:30Z)
• A New Framework for Quantum Phases in Open Systems: Steady State of Imaginary-Time Lindbladian Evolution [18.47824812164327]
  We introduce the concept of imaginary-time Lindbladian evolution as an alternative framework. This new approach defines gapped quantum phases in open systems through the spectrum properties of the imaginary-Liouville superoperator.
  arXiv  Detail & Related papers  (2024-08-06T14:53:40Z)
• Asymptotic Birkhoff-Violation in Operational Theories: Thermodynamic Implications and Information Processing [0.0]
  Renowned Birkhoff-von Neumann theorem identifies source of randomness to be the application of reversible operations on the system under study. Here, we extend this investigation beyond quantum mechanics to a broader class of operational theories described within the framework of general probabilistic theories. We show that Birkhoff-violation in GPTs can lead to consequences that are atypical to quantum theory.
  arXiv  Detail & Related papers  (2024-06-13T04:38:43Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Quantum Algorithms for Open Lattice Field Theory [0.0]
  We develop non-Hermitian quantum circuits and explore their promise on a benchmark, the quantum one-dimensional Ising model with complex longitudinal magnetic field. The development of attractors past critical points in the space of complex couplings indicates a potential for study on near-term noisy hardware.
  arXiv  Detail & Related papers  (2020-12-09T19:00:18Z)
• Relevance of stochasticity for the emergence of quantization [0.0]
  The theories of quantum mechanics and electrodynamics bring to light important aspects of the quantum dynamics that are concealed in the standard formalism. Here we take further work regarding the connection between the two theories to exhibit the role of Quantumity and diffusion in the process leading from the originally classical+zpf regime to the quantum regime.
  arXiv  Detail & Related papers  (2020-10-14T02:24:22Z)
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions [1.2433211248720717]
  The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness. We define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. We demonstrate an equivalent formalism of computation using a general time independent Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-06T07:53:28Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.