Information processing in convex operational theories

Abstract

In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories. One approach to doing this, pioneered by Abramsky and Coecke, is to abstract the essential categorical features of classical and quantum mechanics that support various information-theoretic constraints and possibilities, e.g., the impossibility of cloning in the latter, and the possibility of teleportation in both. Another approach, pursued by the authors and various collaborators, is to begin with a very conservative, and in a sense very concrete, generalization of classical probability theory--which is still sufficient to encompass quantum theory--and to ask which "quantum" informational phenomena can be reproduced in this much looser setting. In this paper, we review the progress to date in this second programme, and offer some suggestions as to how to link it with the categorical semantics for quantum processes developed by Abramsky and Coecke.

15 pages; paper for DCM/QPL (Developments in Computational Models / Quantum Programming Languages) 2008 (Oxford University)

References in corpus (5)

• Unconditionally secure quantum bit commitment is impossible
• Noncommuting mixed states cannot be broadcast
• Non-local correlations as an information theoretic resource
• Is Quantum Bit Commitment Really Possible?
• How to Derive the Hilbert-Space Formulation of Quantum Mechanics From Purely Operational Axioms

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• One simple postulate implies that every polytopic state space is classical
• Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models
• Entanglement and the three-dimensionality of the Bloch ball
• Symmetry and composition in probabilistic theories
• A discussion on the origin of quantum probabilities
• Uncertainty principle certifies genuine source of intrinsic randomness
• Theories of systems with limited information content