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Physical Review A

Squeezed states and Shannon entropy

J. Aliaga, G. Crespo, Araceli N. Proto

Published Jun 1, 1994• 2 citations
Publisher

Abstract

A wave-function approach to the interaction Hamiltonian for the degenerate parametric amplifier has been recently presented [C. G. Bollini and L. E. Oxman, Phys. Rev. A 47, 2339 (1993)]. We want to show here that a maximum entropy principle density matrix approach can be used to reobtain all the results shown in this reference, and also to avoid the use of a nonproperly continuous generalization of the Shannon discrete entropy.

DOI
10.1103/physreva.49.5146

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A wave-function approach to the interaction Hamiltonian for the degenerate parametric amplifier has been recently presented [C. G. Bollini and L. E. Oxman, Phys. Rev. A 47, 2339 (1993)]. We want to show here that a maximum entropy principle density matrix approach can be used to reobtain all the results shown in this reference, and also to avoid the use of a nonproperly continuous generalization of the Shannon discrete entropy.
A method for representing probabilistic aspects of quantum systems by means of a density function on the space of pure quantum states is introduced. In particular, a maximum entropy argument allows us to obtain a natural density function that only reflects the information provided by the density matrix. This result is applied to derive the Shannon entropy of a quantum state. The information theoretic quantum entropy thereby obtained is shown to have the desired concavity property, and to differ from the conventional von Neumann entropy. This is illustrated explicitly for a two-state system. (C) 2000 American Institute of Physics. S0022-2488(00)03305-3.
A method for representing probabilistic aspects of quantum systems by means of a density function on the space of pure quantum states is introduced. In particular, a maximum entropy argument allows us to obtain a natural density function that only reflects the information provided by the density matrix. This result is applied to derive the Shannon entropy of a quantum state. The information theoretic quantum entropy thereby obtained is shown to have the desired concavity property, and to differ from the conventional von Neumann entropy. This is illustrated explicitly for a two-state system.