Entanglement of observables: Quantum conditional probability approach
- URL: http://arxiv.org/abs/2303.12393v1
- Date: Wed, 22 Mar 2023 08:58:15 GMT
- Title: Entanglement of observables: Quantum conditional probability approach
- Authors: Andrei Khrennikov and Irina Basieva
- Abstract summary: It is meaningless to speak about entanglement without pointing to the fixed observables A and B, so this is AB-entanglement.
Dependence of quantum observables is formalized as non-coincidence of conditional probabilities.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper is devoted to clarification of the notion of entanglement through
decoupling it from the tensor product structure and treating as a constraint
posed by probabilistic dependence of quantum observable A and B. In our
framework, it is meaningless to speak about entanglement without pointing to
the fixed observables A and B, so this is AB-entanglement. Dependence of
quantum observables is formalized as non-coincidence of conditional
probabilities. Starting with this probabilistic definition, we achieve the
Hilbert space characterization of the AB-entangled states as amplitude
non-factorisable states. In the tensor product case, $AB$-entanglement implies
standard entanglement, but not vice verse. AB-entanglement for dichotomous
observables is equivalent to their correlation. We describe the class of
quantum states that are A_u B_u-entangled for a family of unitary operators
(u). Finally, observables entanglement is compared with dependence of random
variables in classical probability theory.
Related papers
- 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) - Form of Contextuality Predicting Probabilistic Equivalence between Two Sets of Three Mutually Noncommuting Observables [0.0]
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes.
These pseudocontexts constitute non-orthogonal bases within the Hilbert space, featuring a state-independent sum of probabilities.
The measurement contextuality in this setup arises from the quantum realizations of the hypergraph, which adhere to a specific bound on the linear combination of probabilities.
arXiv Detail & Related papers (2023-09-22T08:51:34Z) - A Universal Quantum Certainty Relation for Arbitrary Number of
Observables [0.0]
We derive by lattice theory a universal quantum certainty relation for arbitrary $M$ observables in $N$-dimensional system.
We find that one cannot prepare a quantum state with PDVs of incompatible observables spreading out arbitrarily.
arXiv Detail & Related papers (2023-08-10T16:44:10Z) - Foundations of non-commutative probability theory (Extended abstract) [1.8782750537161614]
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics.
The sample space has a central role in this presentation and random variables, i.e., observables, are defined in a natural way.
arXiv Detail & Related papers (2023-06-01T20:34:01Z) - Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
We quantify the effects of charges' noncommutation on Page curves.
We show analytically and numerically that the noncommuting-charge case has more entanglement.
arXiv Detail & Related papers (2022-09-28T18:00:00Z) - Conditional probability framework for entanglement and its decoupling
from tensor product structure [0.0]
In Schr"odinger's words, this is entanglement of knowledge which can be extracted via conditional measurements.
We restrict considerations to perfect conditional correlations (PCC) induced by measurements.
One of our aims is to decouple the notion of entanglement from the compound systems.
arXiv Detail & Related papers (2022-05-21T06:30:01Z) - 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) - Why we should interpret density matrices as moment matrices: the case of
(in)distinguishable particles and the emergence of classical reality [69.62715388742298]
We introduce a formulation of quantum theory (QT) as a general probabilistic theory but expressed via quasi-expectation operators (QEOs)
We will show that QT for both distinguishable and indistinguishable particles can be formulated in this way.
We will show that finitely exchangeable probabilities for a classical dice are as weird as QT.
arXiv Detail & Related papers (2022-03-08T14:47:39Z) - Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same.
Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles.
We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
arXiv Detail & Related papers (2021-05-10T13:11:59Z) - Quantum eigenstates from classical Gibbs distributions [0.0]
We discuss how the language of wave functions (state vectors) and associated non-commuting Hermitian operators naturally emerges from classical mechanics.
We show that some paradigmatic examples such as tunneling, band structures, Berry phases, Landau levels, level statistics and quantum eigenstates in chaotic potentials can be reproduced to a surprising precision from a classical Gibbs ensemble.
arXiv Detail & Related papers (2020-07-14T18:00:05Z) - 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)
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.