Physics – Quantum Physics
Scientific paper
2010-06-05
Physics
Quantum Physics
21 pages, 6 figures; Proceedings of Quantum Physics and Logic, Oxford 8-9 April 2009
Scientific paper
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 mix 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.
No associations
LandOfFree
Relating toy models of quantum computation: comprehension, complementarity and dagger mix autonomous categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Relating toy models of quantum computation: comprehension, complementarity and dagger mix autonomous categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Relating toy models of quantum computation: comprehension, complementarity and dagger mix autonomous categories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-637902