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This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1.
Mathematische grundlagen der quantenmechanik
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J. C. Baez and J. Dolan. Higher-dimensional algebra and topological quantum field theory. Journal of Mathematical Physics
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Lectures on Quantum Theory
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H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, and B. Schumacher. Noncommuting mixed states cannot be broadcast. Physical Review Letters,
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A. Joyal, R. Street and D. Verity. Traced monoidal categories. Proceedings of the Cambridge Philosophical Society
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S. Abramsky and B. Coecke. Abstract physical traces. Theory and Applications of Categories
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R. Jozsa. An introduction to measurement based quantum computation, 2005. arXiv:quant-ph/0508124
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L. H. Kauffman. Teleportation topology. Optics and Spectroscopy
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S. Abramsky and R. W. Duncan. A categorical quantum logic. Mathematical Structures in Computer Science
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J. C. Baez. Quantum quandaries: a category-theoretic perspective. In: The Structural Foundations of Quantum Gravity, D. Rickles, S. French and J. T. Saatsi (Eds), pages 240–266. Oxford University Press. arXiv:quant-ph/0404040, 2006
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P. W. Shor. Fault-tolerant quantum computation. In: Proceedings of the 37nd Annual Symposium on Foundations of Computer Science, pages 56–65. IEEE Computer Society Press, 1996
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R. Cockett and R. A. G. Seely. Weakly distributive categories. Journal of Pure and Applied Algebra
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M. F. Atiyah. Topological quantum field theory. Publications Mathématiques de l’IHES
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C. J. Isham and J. Butterfield. Topos perspective on the Kochen-Specker theorem: I. Quantum states as generalized valuations. International Journal of Theoretical Physics
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S. MacLane. Categories for the Working Mathematician. 2nd edition. Springer, 1998
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S. Abramsky, R. Blute and P. Panangaden. Nuclear and trace ideals in tensored
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E. M. Clarke, O. Grumberg and D. Peled. Model Checking. Springer, 1999
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B. Coecke and E. O. Paquette. POVMs and Naimark’s theorem without sums. Electronic Notes in Theoretical Computer Science (To appear). arXiv:quant-ph/0608072, 2006
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L Crane. Categorical geometry and the mathematical foundations of quantum general relativity, 2006. arXiv:gr-qc/0602120v
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R. W. Duncan. Types for Quantum Computing. D.Phil. thesis. University of Oxford, 2006
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R. Houston. Finite products are biproducts in a compact closed category. Journal of Pure and Applied Algebra
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S. Abramsky. Temperley-Lieb algebra: From knot theory to logic and computation via quantum mechanics. In: Mathematics of Quantum Computing and Technology, G. Chen, L. Kauffman and S. Lamonaco (eds), pages 415–458. Taylor and Francis, 2007
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B. Coecke. De-linearizing linearity: projective quantum axiomatics from strong compact closure. Electronic Notes in Theoretical Computer Science
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B. Coecke and D. Pavlovic. Quantum measurements without sums. In: Mathematics of Quantum Computing and Technology, G. Chen, L. Kauffman and S. Lamonaco (eds), pages 567–604. Taylor and Francis, 2007. arXiv:quant-ph/0608035
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V. Danos, E. Kashefi and P. Panangaden. The Measurement Calculus. Journal of the ACM
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A. Doëring and C. J. Isham. A topos foundation for theories of physics: I. Formal languages for physics, 2007. arXiv:quant-ph/0703060
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M. Fiore. An axiomatics and a combinatorial model for creation/annihilation operators and differential structure. Talk given at the workshop on Categorical Quantum Logic, Oxford University, Jul. 2007. Slides available at http://se10.comlab.ox.ac.uk:8080/ FOCS/CQL
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J. Harding, Some quantum logic and a few categories. Talk given at the workshop on Categorical Quantum Logic, Oxford University, Jul. 2007. Slides available at http://se10.comlab.ox.ac.uk:8080/FOCS/CQL
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P. Selinger. Dagger compact categories and completely positive maps. Electronic Notes in Theoretical Computer Science
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R. Spekkens. Evidence for the epistemic view of quantum states: A toy theory. Physical Review A
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R. Street. Quantum Groups: A Path to Current Algebra. Cambridge UP, 207
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S. Abramsky and N. Tzevelekos. Introduction to categories and categorical logic. In: New Structures for Physics, B. Coecke, Ed, Springer lecture Notes in Physics, 2008
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J. C. Baez and M. Stay (2008) Physics, topology, logic and computation: A Rosetta Stone. In: New Structures for Physics, B. Coecke, Ed, Springer lecture Notes in Physics, 2008
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B. Coecke. Axiomatic description of mixed states from Selinger’s CPM-construction. Proceedings of QPL’06. Electronic Notes in Theoretical Computer Science (to appear, 2008)
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B. Coecke and R. W. Duncan. Interacting quantum observables. In: Proceedings of the 35th International Colloquium on Automata, Languages and Programming (ICALP), pages 298–310, Lecture Notes in Computer Science
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B. Coecke and W. A. Edwards. Toy quantum categories. In: Proc. Quantum Physics and Logic/Development of Computational Models (QPL-DCM). Electronic Notes in Theoretical Computer Science, to appear 2008
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B. Coecke, E. O. Paquette and S. Perdrix. Bases in diagramatic quantum protocols. In: Proc. Mathematical Foundations for Programming Semantics XXIV, to appear, 2008
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B. Coecke, D. Pavlovic and J. Vicary. Commutative
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J. Harding. Orthomodularity in dagger biproduct categories. Preprint, 2008
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P. Selinger. Finite dimensional Hilbert spaces are complete for dagger compact closed categories. In: Proc. Quantum Physics and Logic/Development of Computational Models (QPL-DCM). Electronic Notes in Theoretical Computer Science, to appear, 2008
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