Title
Partial Order on Classical and Quantum States: Revised Bayesian Order, Majorization Order, Stochastic Order, characterization of,Used
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In this work we extend the work done by Bob Coecke and Keye Martin in their paper "Partial Order on Classical States and Quantum States (2003)". We review basic notions involving elementary domain theory, the set of probability measures on a finite set {a1, a2, . . . , an}, which we identify with the standard (n1)simplex? n and Shannon Entropy. We consider partial orders on? n, which have the Entropy Reversal Property (ERP) : elements lower in the order have higher (Shannon) entropy or equivalently less information. The ERP property is important because of its applications in quantum information theory. We define a new partial order on? n, called Stochastic Order, using the wellknown concept of majorization order and show that it has the ERP property and is also a continuous domain. In contrast, the bayesian order on? n defined by Coecke and Martin has the ERP property but is not continuous.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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