2009/08/17 by Howard Barnum, Barnum, Howard, Alexander Wilce +1 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.0908.2354
18 pages, grew from presentation in special session on Information in Physics at Mathematical Foundations of Programming Semantics 2007, Tulane University, New Orleans
arxiv created 2009/08/17 · openalex publication_date 2009/08/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review some of our recent results (with collaborators) on information processing in an ordered linear spaces framework for probabilistic theories. These include demonstrations that many "inherently quantum" phenomena are in reality quite general characteristics of non-classical theories, quantum or otherwise. As an example, a set of states in such a theory is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. As another example, information that can be obtained about a system in this framework without causing disturbance to the system state, must be inherently classical. We also review results on teleportation protocols in the framework, and the fact that any non-classical theory without entanglement allows exponentially secure bit commitment in this framework. Finally, we sketch some ways of formulating our framework in terms of categories, and in this light consider the relation of our work to that of Abramsky, Coecke, Selinger, Baez and others on information processing and other aspects of theories formulated categorically.