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arXiv:math/0502024

The maximum entropy state

Keye Martin

Published Feb 1, 2005• 1 citation
arXivHTMLPDF

Abstract

We give an algorithm for calculating the maximum entropy state as the least fixed point of a Scott continuous mapping on the domain of classical states in their Bayesian order.
DOI
10.48550/arxiv.math/0502024

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We propose a new 'quantum domain theory' in which Scott-continuous functions are replaced by Scott-continuous natural transformations. Completely positive maps are widely accepted as a model of first-order quantum computation. We begin by establishing a categorical characterization of completely positive maps as natural families of positive maps. We explore this categorical characterization by building various representations of quantum computation based on different structures: affine maps between cones of positive elements, morphisms of algebras of effects, and affine maps of convex sets of states. By focusing on convex dcpos, we develop a quantum domain theory and show that it supports some important constructions such as tensor products by quantum data, and lifting.
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