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A Partial Order On Classical And Quantum States, Arka Bandyopadhyay

LSU Master's Theses

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 (n-1)-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 …