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Lower and upper probabilities in the distributive lattice of subsystems

A. Vourdas
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Abstract

The set of subsystems of a finite quantum system (with variables in Z(n)) together with logical connectives, is a distributive lattice. With regard to this lattice, the (where P(m) is the projector to) obeys a supermodularity inequality, and it is interpreted as a lower probability in the sense of the Dempster-Shafer theory, and not as a Kolmogorov probability. It is shown that the basic concepts of the Dempster-Shafer theory (lower and upper probabilities and the Dempster multivaluedness) are pertinent to the quantum formalism of finite systems.

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A. Vourdas. 2014-10-08. Lower and upper probabilities in the distributive lattice of subsystems. https://doi.org/10.1088/1751-8113/47/34/345203

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