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Basic Sciences Journal of Textile Universities

The comparabilities between classical states

Gao Rong-fa

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

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.

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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.
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.
The quantum statistical properties of the superposition state, which involve two arbitrary coherent states |β〉 and |mβeiδ〉, are investigated from two aspects, such as the phase distribution and Winger function. The results show that the non-classical properties of the superposition state depend on β2, amplitude coefficient m, the phase difference between the coherent states δ, and the phase difference between the superposition coefficients . When selected suitable parameters the superposition state exhibits quantum effect. The phase distribution and Wigner function of an equally populated mixture of two coherent states are derived, too. By comparison the results show that the presence of the coherence terms makes the superposition state with full quantum-mechanical behavior.