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International Journal of Quantum Information

A STUDY OF STATISTICAL ENSEMBLE USING FUZZY LOGIC AND DENSITY MATRIX

Alauddin Ahmed, Md. Taufiqur Rahman, Mohammad Anwer

Published Dec 16, 2004• 0 citations
Publisher

Abstract

We use fuzzy logic for the probabilistic interpretation of statistical ensemble and compare the result with the density matrix results for quantum entanglement.
DOI
10.1142/s0219749905000517

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In quantum physics, we often need to consider ensembles that are not pure cases, that is, that cannot be described by state vectors. This is so, for instance, when an ensemble is composed of several subensembles that are described by nonequivalent state vectors. It also happens in most cases in which we consider ensembles of definite subsystems of some larger systems. The density matrix—or "statistical operator"—formalism is one that makes it possible to deal with such situations swiftly and efficiently. The rules apply only to ensembles that can be described by state vectors. These rules entail as consequences new expressions for quantum probabilities and mean values, which can be called the—derived— "statistical operator rules." However, it is also possible to formulate the statistical operator rules directly instead. The Heisenberg "uncertainty" relations imply that in general f(x,p) cannot be interpreted as really being a joint probability distribution.
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