Quantaloids Describing Causation and Propagation of Physical Properties |
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Authors: | Bob Coecke David J Moore Isar Stubbe |
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Institution: | (1) Dept. of Mathematics, Free University of Brussels, Pleinlaan 2, B-1050 Brussels, Belgium;(2) Dept. of Theoretical Physics, Université de Genève, Quai Ernest-Ansermet 24, CH-1211 Genève 4, Switzerland;(3) Dépt. de Mathématiques, Université Catholique de Louvain, Ch. du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium |
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Abstract: | A general principle of causal duality for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of causal duality in operational quantum logic. |
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Keywords: | causal duality property lattice Galois adjoint quantaloid |
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