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Minimum relative entropies of low-dimensional spin systems

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  • Slater, Paul B.

Abstract

Work of Band and Park in the mid-1970's in which they proposed — on information-theoretic grounds — an alternative to the von Neumann entropy measure, S(ϱ) = -Tr ϱ ln ϱ, of a density matrix (ϱ) has apparently not been further applied. In this paper, however, specific measures are generated of the information-theoretic entropy of spin-12, spin-1 and two-photon mixed states. For this purpose, the minimum relative entropies of arbitrary mixed states with respect to uniform prior distributions over the pure states are determined. Though Band and Park did not specifically discuss this approach, it is contended that it is harmonious with their position. The duality theory of convex programming is employed to interrelate the von Neumann entropy and the minimum relative entropy measure adopted. Some concluding remarks are made on the possible use of such relative entropy indices in modeling the nonunitary (irreversible) evolution of quantum systems.

Suggested Citation

  • Slater, Paul B., 1992. "Minimum relative entropies of low-dimensional spin systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 182(1), pages 145-154.
    • Handle: RePEc:eee:phsmap:v:182:y:1992:i:1:p:145-154
    DOI: 10.1016/0378-4371(92)90235-I
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    References listed on IDEAS

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    1. P B Slater, 1989. "Maximum-Entropy Representations in Convex Polytopes: Applications to Spatial Interaction," Environment and Planning A, , vol. 21(11), pages 1541-1546, November.
    2. P B Slater, 1987. "Maximum Entropy Convex Decompositions of Doubly Stochastic and Nonnegative Matrices," Environment and Planning A, , vol. 19(3), pages 403-407, March.
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    Cited by:

    1. Porta Mana, PierGianLuca, 2009. "On the relation between plausibility logic and the maximum-entropy principle: a numerical study," OSF Preprints fejvm, Center for Open Science.

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