Theoretical Computer Science
Specifying Interaction Categories
CTCS '97 Proceedings of the 7th International Conference on Category Theory and Computer Science
Towards a quantum programming language
Mathematical Structures in Computer Science
A Categorical Semantics of Quantum Protocols
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Dagger Compact Closed Categories and Completely Positive Maps
Electronic Notes in Theoretical Computer Science (ENTCS)
Interacting Quantum Observables
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Quantum and Classical Structures in Nondeterminstic Computation
QI '09 Proceedings of the 3rd International Symposium on Quantum Interaction
Coalgebras, Chu Spaces, and Representations of Physical Systems
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
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Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical structures, and analyze one layer at a time. It seems natural to combine the two approaches, and several authors have already pursued this idea. We explore categorical comprehension construction as a tool for adding features to toy models. We use it to comprehend quantum propositions and probabilities within the basic model of finite-dimensional Hilbert spaces. We also analyze complementary quantum observables over the category of sets and relations. This leads into the realm of test spaces, a well-studied model. We present one of many possible extensions of this model, enabled by the comprehension construction. Conspicuously, all models obtained in this way carry the same categorical structure, extending the familiar dagger compact framework with the complementation operations. We call the obtained structure dagger mix autonomous, because it extends star autonomous categories, popular in computer science, in a similar way like dagger compact structure extends compact categories. Dagger mix autonomous categories seem to arise quite naturally in quantum computation, as soon as complementarity is viewed as a part of the global structure.