Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Communications in Mathematical Physics

A characterization of the classical states of the quantum harmonic oscillator by means of de Finetti's theorem

Alexander Bach, A. Srivastav

Published Sep 1, 1989• 4 citations
Publisher
DOI
10.1007/bf01238810

Related papers

The simplex structure of the classical states of the quantum harmonic oscillator

Alexander Bach, U. L�xmann-Ellinghaus

Communications in Mathematical Physics•Dec 1, 1986•28 citations

Integral Representations by Means of Coherent States Derived from de Finetti's Theorem

Alexander Bach

It is shown that the simplex of classical states, i.e. the set of those statistical operators which admit an integral representation by means of coherent states, can be explained as a result of the quantum analogue of the Poisson limit of de Finetti's theorem.

Europhysics Letters (EPL)•Aug 15, 1987•7 citations

De Finetti Theorems for Braided Parafermions

Kaifeng Bu, Arthur Jaffe, Zhengwei Liu +1 more

Abstract The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with respect to a natural action of the braid group, and we emphasize the pictorial formulation and interpretation of our results. We prove a new type of de Finetti theorem for the four-string, double-braid group acting on the parafermion algebra to braid qudits, a natural symmetry in the quon language for quantum information. We prove that a braid-invariant state is extremal if and only if it is a product state. Furthermore, we provide an explicit characterization of braid-invariant states on the parafermion algebra, including finding a distinction that depends on whether the order of the parafermion algebra is square free. We characterize the extremal nature of product states (an inverse de Finetti theorem).

arXiv:1805.05990•Communications in Mathematical Physics•Oct 25, 2019•1 citation

Classical phase-space distribution for approximating quantum states of the harmonic oscillator

David Agmon, I. R. Senitzky

Annals of the Israel Physical Society•Jan 1, 1978•0 citations

The de Finetti theorem for test spaces

Jonathan Barrett, Matthew Leifer

We prove a de Finetti theorem for exchangeable sequences of states on test spaces , where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.

arXiv:0712.2265•New Journal of Physics•Mar 17, 2009•27 citations

Harmonic oscillator in a variety of forms of classical and quantum mechanics

Petr Česnek

•Jan 1, 2006•0 citations
Abstract The classical de Finetti theorem in probability theory relates symmetry under the permutation group with the independence of random variables. This result has application in quantum information. Here we study states that are invariant with respect to a natural action of the braid group, and we emphasize the pictorial formulation and interpretation of our results. We prove a new type of de Finetti theorem for the four-string, double-braid group acting on the parafermion algebra to braid qudits, a natural symmetry in the quon language for quantum information. We prove that a braid-invariant state is extremal if and only if it is a product state. Furthermore, we provide an explicit characterization of braid-invariant states on the parafermion algebra, including finding a distinction that depends on whether the order of the parafermion algebra is square free. We characterize the extremal nature of product states (an inverse de Finetti theorem).
We prove a de Finetti theorem for exchangeable sequences of states on test spaces , where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.