Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy

• URL: http://arxiv.org/abs/2202.02076v1
• Date: Fri, 4 Feb 2022 11:19:15 GMT
• Title: Quantum Central Limit Theorems, Emergence of Classicality and Time-dependent Differential Entropy
• Authors: Tien D. Kieu
• Abstract summary: We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite distribution for the expectation values of observables. These probability distributions open some pathway for an emergence of classical behaviours in the limit of infinitely large number of identical and non-interacting quantum constituents. This is in contradistinction to other mechanisms of classicality emergence due to environmental decoherence and consistent histories. The probability distributions so derived also enable us to evaluate the nontrivial time-dependence of certain differential entropies.

Related papers

• From Quantum-Mechanical Acceleration Limits to Upper Bounds on Fluctuation Growth of Observables in Unitary Dynamics [0.0]
  Quantum Speed Limits (QSLs) are fundamentally linked to the tenets of quantum mechanics, particularly the energy-time uncertainty principle. Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians.
  arXiv  Detail & Related papers  (2025-03-31T22:14:16Z)
• 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)
• Precision bounds for multiple currents in open quantum systems [37.69303106863453]
  We derivation quantum TURs and KURs for multiple observables in open quantum systems undergoing Markovian dynamics. Our bounds are tighter than previously derived quantum TURs and KURs for single observables. We also find an intriguing quantum signature of correlations captured by the off-diagonal element of the Fisher information matrix.
  arXiv  Detail & Related papers  (2024-11-13T23:38:24Z)
• Symmetry operations and Critical Behaviour in Classical to Quantum Stochastic Processes [0.0]
  We generate a large class of self contained quantum extensions by operations. We show that the relaxation processes for different quantum extensions are different and that is supported by the measure of coherence.
  arXiv  Detail & Related papers  (2024-09-14T03:01:54Z)
• Proposal of an optical Bell's experiment to test the boundary between determinism and indeterminism in Quantum Mechanics [41.94295877935867]
  It was recently noted the existence of an apparently discontinuous boundary between determinism and indeterminism in Quantum Mechanics. We propose to explore this boundary by recording the distribution of outcomes of a given parity interrupted by outcomes of the other parity. The features of these distributions for small rotations of the angle settings near critical points may indicate whether the underlying process is in-deterministic or not.
  arXiv  Detail & Related papers  (2024-08-20T14:48:08Z)
• On the evolution of expected values in open quantum systems [44.99833362998488]
  We identify three factors contributing to the evolution of expected values. In some cases, the non-thermal contributions to the energy rate of change can be expressed as the expected value of a Hermitian operator.
  arXiv  Detail & Related papers  (2024-02-29T06:47:28Z)
• Asymmetry and tighter uncertainty relations for R\'enyi entropies via quantum-classical decompositions of resource measures [0.0]
  It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is discussed.
  arXiv  Detail & Related papers  (2023-04-12T08:49:48Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Role of boundary conditions in the full counting statistics of topological defects after crossing a continuous phase transition [62.997667081978825]
  We analyze the role of boundary conditions in the statistics of topological defects. We show that for fast and moderate quenches, the cumulants of the kink number distribution present a universal scaling with the quench rate.
  arXiv  Detail & Related papers  (2022-07-08T09:55:05Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• 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)
• A quantum prediction as a collection of epistemically restricted classical predictions [0.0]
  We show how the quantum description of an experiment can be decomposed into classical descriptions. One recovers the quantum prediction via a simple but highly nonclassical rule.
  arXiv  Detail & Related papers  (2021-07-06T16:55:54Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Theory of Ergodic Quantum Processes [0.0]
  We consider general ergodic sequences of quantum channels with arbitrary correlations and non-negligible decoherence. We compute the entanglement spectrum across any cut, by which the bipartite entanglement entropy can be computed exactly. Other physical implications of our results are that most Floquet phases of matter are metastable and that noisy random circuits in the large depth limit will be trivial as far as their quantum entanglement is concerned.
  arXiv  Detail & Related papers  (2020-04-29T18:00:03Z)

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.