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

Journal of Shangluo University

The Distance Between Two Multi-mode Coherent States

Chen Yong-zhuang

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

The distance D(rj rj′ θj) between the two multi-mode coherent state |Z1q and |Z′2q is studied. Relationships between D(rj rj′ θj) and parameters amount D(rj rj′ θj) are discussed carefully. It is found that the size of the D(rj rj′ θj) has relation with the distance of every coherent state which displaced in complex space and it represents cyclically mutation with their initialy phases differential θ changing under some condition.

Related papers

The Distance Between Multi-mode Vacuum States and Multi-mode Coherent States

Ying Li

Based on Ludwig Knoll et. al. definition, the general distance function D(rj) between multi-mode vacuum state and multi-mode coherent state is got. A ccoding to D (rj) relationships about distance function and parameters of multi -mode vacuum state and multi -mode coherent state are discussed in this paper, differentiates of multi-mode vacuum state and multi-mode coherent state is proved.

Journal of Shangluo University•Jan 1, 2003•0 citations

The comparabilities between classical states

Gao Rong-fa

Based on the Ludwig Knll s general definition of distance function of which is between two quantum states, the general distance function between the two coherent state |β1,|β2 , vacuum state and coherent state are studied. The relationships amount this distance and the parameters of states are discussed carefully. It is find that the similitude degrees of states |β1 and |β2 correlate with distance of every distance which is moved in complex space, and D(β1,β2) represents cyclically mutation with their initially phases differential Δ θ changing under some condition.If distance is displaced very small, coherent state is same as vacuum state.

Basic Sciences Journal of Textile Universities•Jan 1, 2003•0 citations

Analyzing on Separability of Two Different Multi-mode Even Coherent State Light Fields

Ying Li

The distance functions Do(rj,rj')which is between two different multi-mode even coherent state light fields is obtained by using the concept of Ludwig Kn?芽ll's et.al.defined.Based on De(rj rj'),the separability of multi-mode even coherent sate light fields is analyzed by the multi-mode coherent state light fields these build up them.

Journal of Shangluo University•Jan 1, 2005•0 citations

The Distance for coherent states and their superposition stetes

Gao Rong-fa

Ganeral distance function D (r,r_0,φ).between a coherent state |α_0and a superposition cpjeremt state of stidoed nu Ludwig Knll's definition.Acorrding to D (r,r_0, φ),the separabiloity relationship amount |α_0 to)and |Ψ are dicussed.It's found that the simiilitude degrees of |α_0)and |Ψ correlete wity distance of every coherent state is displaced in copmlex plane the difference of |α_0 and |Ψand superposition phase;The similitudes of odd,even and |α_0and |Ψ are studied carefully.

Journal of Shangluo University•Jan 1, 2004•0 citations

Mode displacements in multimode systems and applications to entanglement

Apostol Vourdas

A $d$-mode system is considered and the concepts of mode-position operator and mode-momentum operator are introduced. Their eigenvalues are integers in ${Z}_{d}$ and the mode phase space is ${Z}_{d}\ifmmode\times\else\texttimes\fi{}{Z}_{d}$. The exponentials of these operators are displacement operators in the mode phase space and they form a Heisenberg-Weyl group. The displacement operators perform a cyclic permutation of a state among the $d$ modes; and they also change its mode momentum (i.e., the rate with which this cyclic permutation takes place). In the case of entangled states the mode displacement operators permute the entanglement among the $d$ observers; and they also change the momentum with which the entanglement propagates.

Physical Review A•Apr 26, 2005•2 citations

Hilbert-Schmidt distance and non-classicality of states in quantum optics

V. V. Dodonov, Olga V. Man’ko, Vladimir I. Man’ko +1 more

The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operator and the squared deviation of the mean values of the number operator for the considered state and the Fock state. Possible modifications in the definition of non-classicality for mixed states with dependence on the impurity parameter and by including the displaced thermal states as the most classical reference states are discussed.

Journal of Modern Optics•Mar 1, 2000•156 citations
The distance D(rj rj′ θj) between the two multi-mode coherent state |Z1q and |Z′2q is studied. Relationships between D(rj rj′ θj) and parameters amount D(rj rj′ θj) are discussed carefully. It is found that the size of the D(rj rj′ θj) has relation with the distance of every coherent state which displaced in complex space and it represents cyclically mutation with their initialy phases differential θ changing under some condition.
Based on the Ludwig Knll s general definition of distance function of which is between two quantum states, the general distance function between the two coherent state |β1,|β2 , vacuum state and coherent state are studied. The relationships amount this distance and the parameters of states are discussed carefully. It is find that the similitude degrees of states |β1 and |β2 correlate with distance of every distance which is moved in complex space, and D(β1,β2) represents cyclically mutation with their initially phases differential Δ θ changing under some condition.If distance is displaced very small, coherent state is same as vacuum state.
Ganeral distance function D (r,r_0,φ).between a coherent state |α_0and a superposition cpjeremt state of stidoed nu Ludwig Knll's definition.Acorrding to D (r,r_0, φ),the separabiloity relationship amount |α_0 to)and |Ψ are dicussed.It's found that the simiilitude degrees of |α_0)and |Ψ correlete wity distance of every coherent state is displaced in copmlex plane the difference of |α_0 and |Ψand superposition phase;The similitudes of odd,even and |α_0and |Ψ are studied carefully.
A ddd-mode system is considered and the concepts of mode-position operator and mode-momentum operator are introduced. Their eigenvalues are integers in Zd{Z}_{d}Zd​ and the mode phase space is ${Z}_{d}\ifmmode\times\else\texttimes\fi{}{Z}_{d}$. The exponentials of these operators are displacement operators in the mode phase space and they form a Heisenberg-Weyl group. The displacement operators perform a cyclic permutation of a state among the ddd modes; and they also change its mode momentum (i.e., the rate with which this cyclic permutation takes place). In the case of entangled states the mode displacement operators permute the entanglement among the ddd observers; and they also change the momentum with which the entanglement propagates.
The Hilbert—Schmidt distance between two arbitrary normalizable states is discussed as a measure of the similarity of the states. Unitary transformations of both states with the same unitary operator (e.g. the displacement of both states in the phase plane by the same displacement vector and squeezing of both states) do not change this distance. The nearest distance of a given state to the whole set of coherent states is proposed as a quantitative measure of non-classicality of the state which is identical when considering the coherent states as the most classical ones among pure states and the deviations from them as non-classicality. The connection to other definitions of the non-classicality of states is discussed. The notion of distance can also be used for the definition of a neighbourhood of considered states. Inequalities for the distance of states to Fock states are derived. For given neighbourhoods, they restrict common characteristics of the state as the dispersion of the number operator and the squared deviation of the mean values of the number operator for the considered state and the Fock state. Possible modifications in the definition of non-classicality for mixed states with dependence on the impurity parameter and by including the displaced thermal states as the most classical reference states are discussed.