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 Theoretical Physics

New Application of Weyl Correspondence in Studying Husimi Operator

Fan Hong‐Yi, Qin Guo, Ma Shan-Jun

Published Jan 1, 2008• 0 citations
Publisher

Abstract

In this paper, the so-called Husimi operator Δ h ( q , p ; κ), which is introduced by smoothing out the Wigner operator Δ w ( q , p ) by averaging over the "coarse graining" function exp[-κ( q '- q ) 2 - ( p ' - p ) 2 /κ], is now regarded as a Weyl correspondence connecting the Husimi operator Δ h ( q , p ; κ) with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify | p , q ;κ⟩ such that Δ h ( q , p ;κ) = | p , q ;κ⟩ ⟨ p , q ;κ|, where | p , q ; κ⟩ is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to find the Husimi operator is presented.

DOI
10.1088/0253-6102/49/1/14

Related papers

Generalized Positive-Definite Operator in Quantum Phase Space Obtained by Virtue of the Weyl Quantization Rule

Liyun Hu, Fan Hong‐Yi

We introduce a generalized positive-definite operator Δ g (q,p) by smoothing out the Wigner operator Δ w (q,p) and by averaging over the “coarse graining" function. The function is then regarded as the classical Weyl correspondence of the operator Δ g (q,p); in this way we can easily identify a quantum state |Φ〉 such that Δ g (q,p) = |Φ〉 〈Φ|, and |Φ〉 turns out to be a new kind of squeezed coherent state. Correspondingly, the generalized distribution function for any state |Ψ〉 is 〈Ψ|Δ g (q,p)|Ψ〉 = |〈Φ|Ψ〉| 2 , which is obviously positive-definite and is a generalization of the Husimi function.

Chinese Physics Letters•Jun 1, 2009•9 citations

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

Fan, Hong-Yi, Liu . +1 more

我们发现一个新κ-参数挤压了协调州的| p ， q > _κ 表示，它拥有行为优良特征，即，它的 Wigner 功能“ s 边缘的分发在”q方向“并且在里面”p方向“是 Gaussian 形式 exp {-κ(q''- q )~ 2 }，并且 exp {( p ”-p)~2/κ},分别地。基于这， | p 的 Husimi 功能， q > _ κ也被获得，它是 Gaussian 拓宽 Wigner 功能的版本。| p， q > _ κ状态为学习 Husimi 操作员的各种各样的性质提供一个好代表性的空格。

理论物理通讯：英文版•Jan 1, 2007•2 citations

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

Fan Hong‐Yi, Liu Shu-Guang

We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.

Communications in Theoretical Physics•Mar 1, 2007•12 citations

New Application of Weyl Correspondence in Studying Husimi Operator

Fan, Hong-Yi, Guo - +3 more

(q,p;κ)=| p， q； κ p， q； κ|| p， q；κ 是挤压的协调状态的一种新类型。纠缠的 Husimi 操作员也这样被对待。因此，发现 Husimi 操作员的一个简单方法被介绍。

理论物理通讯：英文版•Jan 1, 2008•0 citations

Husimi operator and Husimi function for describing electron's probability distribution in uniform magnetic field derived by virtue of the entangled state representation

Hong-Yi Fan, Qin Guo

For the first time we introduce the Husimi operator Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase space(gamma,varepsilon) for electron's states in uniform magnetic field, where kappa is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301 (2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa kappa

arXiv:quant-ph/0611206•Nov 20, 2006•1 citation

Transform relations between squeezed coherent state representation and quantum phase space distribution functions

Liang Xiu-Dong, Tai Yun-Jiao, Cheng Jian-Min +2 more

A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.

Acta Physica Sinica•Jan 1, 2015•0 citations
In this paper, the so-called Husimi operator Δ h ( q , p ; κ), which is introduced by smoothing out the Wigner operator Δ w ( q , p ) by averaging over the "coarse graining" function exp[-κ( q '- q ) 2 - ( p ' - p ) 2 /κ], is now regarded as a Weyl correspondence connecting the Husimi operator Δ h ( q , p ; κ) with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify | p , q ;κ⟩ such that Δ h ( q , p ;κ) = | p , q ;κ⟩ ⟨ p , q ;κ|, where | p , q ; κ⟩ is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to find the Husimi operator is presented.
We introduce a generalized positive-definite operator Δ g (q,p) by smoothing out the Wigner operator Δ w (q,p) and by averaging over the “coarse graining" function. The function is then regarded as the classical Weyl correspondence of the operator Δ g (q,p); in this way we can easily identify a quantum state |Φ〉 such that Δ g (q,p) = |Φ〉 〈Φ|, and |Φ〉 turns out to be a new kind of squeezed coherent state. Correspondingly, the generalized distribution function for any state |Ψ〉 is 〈Ψ|Δ g (q,p)|Ψ〉 = |〈Φ|Ψ〉| 2 , which is obviously positive-definite and is a generalization of the Husimi function.
我们发现一个新κ-参数挤压了协调州的| p ， q > _κ 表示，它拥有行为优良特征，即，它的 Wigner 功能“ s 边缘的分发在”q方向“并且在里面”p方向“是 Gaussian 形式 exp {-κ(q''- q )~ 2 }，并且 exp {( p ”-p)~2/κ},分别地。基于这， | p 的 Husimi 功能， q > _ κ也被获得，它是 Gaussian 拓宽 Wigner 功能的版本。| p， q > _ κ状态为学习 Husimi 操作员的各种各样的性质提供一个好代表性的空格。
We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.
For the first time we introduce the Husimi operator Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase space(gamma,varepsilon) for electron's states in uniform magnetic field, where kappa is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301 (2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa kappa
A new operator representation, called squeezed coherent state representation, is introduced since Husimi operator has the form of squeezed coherent state. We fisrt introduce its specific integral expression. When κ = 1, this representation is reduced to the usual P function. As an example, we calculate the squeezed coherent state representation for thermal field to illustrate a difference between P function and the squeezed coherent state representation. Especially, in order to better apply this representation to quantum optics, we reveal the integral transformations between the squeezed coherent state representation, respectively, and the following three functions: Wigner function, Q function, and Husimi function.