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2012): Symmetry and selfduality in categories of probabilistic models
 Proceedings of QPL 2011, Series 95
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Perspectives on the Formalism of Quantum Theory
, 2012
"... The contents of Chapter Three are based on a collaboration led by Markus Müller, and in particular the publication: • M. P. Müller and C. Ududec. “The structure of reversible computation determines the selfduality of quantum theory. ” Phys. Rev. Lett., 108(13):130401 (2012), with the manuscript ..."
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The contents of Chapter Three are based on a collaboration led by Markus Müller, and in particular the publication: • M. P. Müller and C. Ududec. “The structure of reversible computation determines the selfduality of quantum theory. ” Phys. Rev. Lett., 108(13):130401 (2012), with the manuscript largely prepared by Müller. Passages and figures have been adapted for inclusion here with his consent. In particular, the results in Section 3.1 are translations from reference [102] made by myself with the help of Google Translate. The results in Section 3.2 were proved by myself. The concept of “bit symmetry ” was introduced Müller. Results 3.23 and 3.24 were largely proved by Müller. The contents of Chapter Four are based on a collaboration with Howard Barnum and Joseph Emerson, which was led by myself. Sections 4.1–4.7 are partially based on the publication:
Symmetry and SelfDuality in Categories of Probabilistic Models
"... This note adds to the recent spate of derivations of the probabilistic apparatus of finitedimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic structure of finitedimensional quantum theory. The derivation rel ..."
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This note adds to the recent spate of derivations of the probabilistic apparatus of finitedimensional quantum theory from various axiomatic packages. We offer two different axiomatic packages that lead easily to the Jordan algebraic structure of finitedimensional quantum theory. The derivation relies on the KoecherVinberg Theorem, which sets up an equivalence between orderunit spaces having homogeneous, selfdual cones, and formally real Jordan algebras. 1