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
- 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) - 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) - Estimation independence as an axiom for quantum uncertainty [0.0]
We show that a plausible principle of estimation independence, which requires that the estimation of momentum of one system must be independent of the position of another system, singles out the specific forms of the estimator.
arXiv Detail & Related papers (2020-05-12T07:12:17Z) - 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.