A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
De-linearizing Linearity: Projective Quantum Axiomatics From Strong Compact Closure
Electronic Notes in Theoretical Computer Science (ENTCS)
Dagger Compact Closed Categories and Completely Positive Maps
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstract scalars, loops, and free traced and strongly compact closed categories
CALCO'05 Proceedings of the First international conference on Algebra and Coalgebra in Computer Science
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These lecture notes survey some joint work with Samson Abramsky as it was presented by me at Mathematical Foundations of Programming Semantics XXI in Birmingham (2005). It concerns a categorical semantics for quantum mechanics introduced in [Abramsky, S. and Coecke, B. (2004) A categorical semantics of quantum protocols. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LiCS'04), IEEE Computer Science Press. An extended & improved version is available at http://arXiv.org/quant-ph/0402130; Abramsky, S. and Coecke, B. (2005) Abstract physical traces. Theory and Applications of Categories 14, 111-124. Available at www.tac.mta.ca/tac/volumes/14/6/14-06abs.html]. We present this semantics with a particular focus on the connection between categorical diagrams and certain pictures involving typed squares, triangles, diamonds and lines. Along the way we unravel the structural components which come with strong compact closure. We provide pointers to related literature. Keywords: Strong compact closure, semantics, quantum mechanics, quantum logic, quantum informatics.