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Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State

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Abstract

The present paper deals with the study of conditional entropy and its properties in a quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. First, we obtained a pseudo-metric on the family of all partitions of the couple (B,s), where B is a Boolean algebra and s is a state on B. This pseudo-metric turns out to be a metric (called the Rokhlin metric) by using a new notion of s-refinement and by identifying those partitions of (B,s) which are s-equivalent. The present theory has then been extended to the quantum space (L,s), where L is an orthomodular lattice and s is a Bayessian state on L. Applying the theory of commutators and Bell inequalities, it is shown that the couple (L,s) can be equivalently replaced by a couple (B,s 0), where B is a Boolean algebra and s 0 is a state on B.

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Authors and Affiliations

  1. Department of Mathematics, University of Allahabad, Allahabad, 211 001, India

    Mona Khare & Shraddha Roy

  2. Allahabad Mathematical Society, 10 C.S.P. Singh Marg, Allahabad, 211 001, India

    Mona Khare & Shraddha Roy

Authors
  1. Mona Khare
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  2. Shraddha Roy
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Correspondence to Mona Khare.

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Khare, M., Roy, S. Conditional Entropy and the Rokhlin Metric on an Orthomodular Lattice with Bayessian State. Int J Theor Phys 47, 1386–1396 (2008). https://doi.org/10.1007/s10773-007-9581-1

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  • DOI: https://doi.org/10.1007/s10773-007-9581-1

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