A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Environment and classical channels in categorical quantum mechanics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Bicategorical Semantics for Nondeterministic Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Topological Structure of Quantum Algorithms
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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We propose a higher semantics for the description of quantum protocols, which deals with quantum and classical information in a unified way. Central to our approach is the modelling of classical data by information transfer to the environment, and the use of 2-category theory to formalize the resulting framework. This 2-categorical semantics has a graphical calculus, the diagrams of which correspond exactly to physically-implementable quantum procedures. Quantum teleportation in its most general sense is reformulated as the ability to remove correlations between a quantum system and its environment, and is represented by an elegant graphical identity. We use this new formalism to describe two new families of quantum protocols.