Identifier
etd-07072011-231500
Degree
Master of Science in Computer Science (MSCS)
Department
Computer Science
Document Type
Thesis
Abstract
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 define a new partial order on ∆n, called Stochastic Order , using the well-known 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.
Date
2011
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Bandyopadhyay, Arka, "A partial order on classical and quantum states" (2011). LSU Master's Theses. 694.
https://repository.lsu.edu/gradschool_theses/694
Committee Chair
Kundu, Sukhamay
DOI
10.31390/gradschool_theses.694