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Chinese Journal of Quantum Electronics

The Wehrl's Entropy and Shannon's Entropy for Superposition Coherent States

Pla Jinan

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

We studied the Wehrl's entropy and Shannon's entropy for superposition coherent states and discussed the relations. It is shown that the entropies are dependent on the superposition coefficient. We point out that the superposition coefficient has great effects on the Shannon's entropy.

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The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schr\\"odinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q-function. Compact-form formulae for the entropic measures are found for superpositions of well-separated states. Examples of Schr\\"odinger cats (including even, odd and Yurke-Stoler coherent states), as well as the cat-like states generated in Kerr medium are analyzed in detail. It is shown that, in contrast to the Wehrl entropy, the Wehrl phase distribution properly distinguishes between different superpositions of unequally-weighted states in respect to their number and phase-space configuration.
The Wehrl information entropy and its phase density, the so-called Wehrl phase distribution, are applied to describe Schrödinger cat and cat-like (kitten) states. The advantages of the Wehrl phase distribution over the Wehrl entropy in a description of the superposition principle are presented. The entropic measures are compared with a conventional phase distribution from the Husimi Q -function. Compact-form formulae for the entropic measures are found for superpositions of well separated states. Examples of Schrödinger cats (including even, odd and Yurke-Stoler coherent states), as well as the cat-like states generated in the Kerr medium, are analysed in detail. It is shown that, in contrast to the Wehrl entropy, the Wehrl phase distribution properly distinguishes between different superpositions of unequally weighted states with respect to their number and phase-space configuration.
In this paper the superpositions of two arbitrary coherent states |Ψ〉 = a |β〉 + b e iϕ |mβe iδ 〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.
The Wehrl’s entropy of the Schrödinger-cat states has been calculated numerically in this paper. In particular, we show the dependence of the Wehrl’s entropy on the two parameters of the Schrödinger-cat states, which act as, respectively, the photon number parameter and the phase difference . The Wehrl’s entropy has been found to be in the range , and its changes with respect to are not homogenized. Furthermore, we obtain both the dependence of the Wehrl’s entropy on the average photon number and the relation between the Wehrl’s entropy and the statistical entropy.