A Free Object in Quantum Information Theory

We consider three examples of affine monoids. The first stems from information theory and provides a natural model of image distortion, as well as a higher-dimensional analogue of a binary symmetric channel. The second, from physics, describes the process of teleporting quantum information with a gi...

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Hauptverfasser:	Martin, Keye, Feng, Johnny, Krishnan, Sanjeevi
Format:	Report
Sprache:	eng
Schlagworte:	AFFINE MONOID BINARY PROCESSORS CATEGORY Cybernetics DISTORTION FREE OBJECT Information Science INFORMATION THEORY INFORMATION TRANSFER MATHEMATICS PHYSICS QUANTUM CHANNEL QUANTUM THEORY Quantum Theory and Relativity SYMMETRY TELEPORTATION
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Zusammenfassung:	We consider three examples of affine monoids. The first stems from information theory and provides a natural model of image distortion, as well as a higher-dimensional analogue of a binary symmetric channel. The second, from physics, describes the process of teleporting quantum information with a given entangled state. The third is purely a mathematical construction, the free affine monoid over the Klein four group. We prove that all three of these objects are isomorphic. Presented at the Conference on Mathematical Foundations of Programming Semantics (MFPS 2010) (26th), held in Ottawa, Canada, on 6-10 May 2010. Published in Electronic Notes in Theoretical Computer Science, v265 p35-47, 6 Sep 2010.