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

Applied Mathematics & Information Sciences

Some Statistical Quantities of a Quantum System in Hypergeometric and Negative Hypergeometric Distributions

Ali Algarni, S. Abdel‐Khalek

Published Feb 18, 2016• 2 citations
Publisher
DOI
10.18576/amis/100225

Related papers

Dynamical Properties of Some Statistical Quantities for a Quantum System in Generalized Negative Binomial States

Ali Algarni, Abdullah M. Almarashi, S. Abdel‐Khalek

Journal of Russian Laser Research•Mar 1, 2018•3 citations

Phase properties of hypergeometric states and negative hypergeometric states

Xiao-Guang Wang

We show that the three quantum states (Pólya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediate states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitian-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the phase probability distribution exhibits one peak for the hypergeometric states and multiple peaks for the negative hypergeometric states.

arXiv:quant-ph/9905029•Journal of Optics B Quantum and Semiclassical Optics•Jan 19, 2000•11 citations

On Generalized Quantum Statistics

Władysław Marcinek

Lecture notes in physics•Jan 1, 2000•2 citations

Generalized hypergeometric coherent states

Thomas Appl, Diethard H Schiller

We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disc and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg–Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces as well as generalized hypergeometric Husimi distributions and corresponding phase distributions.

arXiv:quant-ph/0308013•Journal of Physics A Mathematical and General•Feb 4, 2004•29 citations

General Properties of the Quantum Statistics

Springer eBooks•Jan 20, 2006•0 citations

Generalized Hypergeometric Coherent States

Appl, T, Schiller, D H

We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disk, and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce generalized hypergeometric Husimi distributions and corresponding phase distributions as well as new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces.

•Aug 1, 2003•17 citations
We show that the three quantum states (Pólya states, the generalized non-classical states related to Hahn polynomials and negative hypergeometric states) introduced recently as intermediate states which interpolate between the binomial states and negative binomial states are essentially identical. By using the Hermitian-phase-operator formalism, the phase properties of the hypergeometric states and negative hypergeometric states are studied in detail. We find that the phase probability distribution exhibits one peak for the hypergeometric states and multiple peaks for the negative hypergeometric states.
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disc and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg–Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces as well as generalized hypergeometric Husimi distributions and corresponding phase distributions.
We introduce a large class of holomorphic quantum states by choosing their normalization functions to be given by generalized hypergeometric functions. We call them generalized hypergeometric states in general, and generalized hypergeometric coherent states in particular, if they allow a resolution of unity. Depending on the domain of convergence of the generalized hypergeometric functions, we distinguish generalized hypergeometric states on the plane, the open unit disk, and the unit circle. All states are eigenstates of suitably defined lowering operators. We then study their photon number statistics and phase properties as revealed by the Husimi and Pegg-Barnett phase distributions. On the basis of the generalized hypergeometric coherent states we introduce generalized hypergeometric Husimi distributions and corresponding phase distributions as well as new analytic representations of arbitrary quantum states in Bargmann and Hardy spaces.