Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability

• URL: http://arxiv.org/abs/2204.11680v4
• Date: Fri, 31 Mar 2023 13:01:26 GMT
• Title: Coherent Fluctuations in Noisy Mesoscopic Systems, the Open Quantum SSEP and Free Probability
• Authors: Ludwig Hruza and Denis Bernard
• Abstract summary: We show the dynamics of fluctuations of coherences in Q-SSEP have a natural interpretation as free cumulants. We show how the link to free probability theory can be used to derive the time evolution of connected fluctuations of coherences.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Quantum coherences characterise the ability of particles to quantum mechanically interfere within some given distances. In the context of noisy many-body quantum systems these coherences can fluctuate. A simple toy model to study such fluctuations in an out-of-equilibrium setting is the open quantum symmetric simple exclusion process (Q-SSEP) which describes spinless fermions in one dimension hopping to neighbouring sites with random amplitudes coupled between two reservoirs. Here we show that the dynamics of fluctuations of coherences in Q-SSEP have a natural interpretation as free cumulants, a concept from free probability theory. Based on this insight we provide heuristic arguments why we expect free probability theory to be an appropriate framework to describe coherent fluctuations in generic mesoscopic systems where the noise emerges from a coarse-grained description. In the case of Q-SSEP we show how the link to free probability theory can be used to derive the time evolution of connected fluctuations of coherences as well as a simple steady state solution.

Related papers

• Deriving the Landauer Principle From the Quantum Shannon Entropy [0.0]
  We derive an expression for the equilibrium probability distribution of a quantum state in contact with a noisy thermal environment. We show that the free energy required to erase or reset a qubit depends sensitively on both the fidelity of the target state and on the physical properties of the environment.
  arXiv  Detail & Related papers  (2024-10-08T07:01:37Z)
• Bath Dynamical Decoupling with a Quantum Channel [44.99833362998488]
  We generalize the notion of dynamical decoupling to repeated kicks with a quantum channel. We find that bath dynamical decoupling works if and only if the kick is ergodic.
  arXiv  Detail & Related papers  (2024-09-27T07:47:52Z)
• Quantum Chaos and Coherence: Random Parametric Quantum Channels [0.0]
  We quantify interplay between quantum chaos and decoherence away from the semi-classical limit. We introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment.
  arXiv  Detail & Related papers  (2023-05-30T18:00:06Z)
• Exact Entanglement in the Driven Quantum Symmetric Simple Exclusion Process [0.0]
  Entanglement properties of driven quantum systems can potentially differ from the equilibrium situation due to long range coherences. We derive exact formulae for its mutual information between different subsystems in the steady state and show that it satisfies a volume law. Surprisingly, the QSSEP entanglement properties only depend on data related to its transport properties and we suspect that such a relation might hold for more general mesoscopic systems.
  arXiv  Detail & Related papers  (2023-04-21T14:37:14Z)
• Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning [47.991114317813555]
  Quantum models implement implicit probabilistic predictors that produce multiple random decisions for each input through measurement shots. This paper proposes to leverage such randomness to define prediction sets for both classification and regression that provably capture the uncertainty of the model.
  arXiv  Detail & Related papers  (2023-04-06T22:05:21Z)
• Theory-independent randomness generation with spacetime symmetries [0.0]
  We introduce a class of semi-device-independent protocols based on the breaking of spacetime symmetries. In particular, we characterise how the response of physical systems to spatial rotations constrains the probabilities of events that may be observed. Our results allow for the generation of secure random numbers without trusting the devices or assuming quantum theory.
  arXiv  Detail & Related papers  (2022-10-26T15:59:10Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• A free energy principle for generic quantum systems [0.0]
  We show how generic quantum systems can be regarded as observers, which with the standard freedom of choice assumption become agents capable of assigning semantics to observational outcomes. We suggest that biological systems employ quantum coherence as a computational resource and - implicitly - as a communication resource.
  arXiv  Detail & Related papers  (2021-12-30T23:34:04Z)
• 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)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)

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.