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Recently, the author and Bob Coecke have introduced a categorical formulation of Quantum Mechanics.
Mathematische Grundlagen der Quantenmechanik
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S. Abramsky and R. W. Duncan. Categorical Quantum Logic. Mathematical Structures in Computer Science
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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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S. Abramsky and B. Coecke. Physical traces: Quantum vs. classical information processing. Electronic Notes in Theoretical Computer Science
2003
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S. Abramsky. High-level methods for quantum computation and information. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pages 410–414. IEEE Computer Science Press, 2004
2004
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S. Abramsky and B. Coecke. A categorical semantics of quantum protocols. In: Proceedings of 19th IEEE conference on Logic in Computer Science, pages 415–425. IEEE Press. arXiv:quant-ph/0402130, 2004
2004
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S. Abramsky. Abstract scalars, loops, and free traced and strongly compact closed categories. In: Proceedings of CALCO 2005, pages 1–31. Lecture Notes in Computer Science
2005
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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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P. Selinger. Dagger compact categories and completely positive maps. Electronic Notes in Theoretical Computer Science
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S. Abramsky and B. Coecke. Categorical Quantum Mechanics. To appear in Handbook of Quantum Logic Vol. II, D. Gabbay and K. Engesser (ed), Elsevier, 2008
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
2008
Later among the works it cites.