Geodesic
CP^∞ and beyond: 2-categorical dilation theory
Theory and applications of categories, Tome 41 (2024), pp. 1783-1811.

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The problem of extending the insights and techniques of categorical quantum mechanics to infinite-dimensional systems was considered in (Coecke and Heunen, 2016). In that work the CP^∞-construction, which recovers the category of Hilbert spaces and quantum operations from the category of Hilbert spaces and bounded linear maps, was defined. Here we show that by a `horizontal categorification' of the CP^∞-construction, one can recover the category of all von Neumann algebras and channels (normal unital completely positive maps) from the 2-category of von Neumann algebras, bimodules and intertwiners. As an application, we extend Choi's characterisation of extremal channels between finite-dimensional matrix algebras to a characterisation of extremal channels between arbitrary von Neumann algebras.
Publié le :
Classification : 18N10, 47A20, 81P47
Keywords: 2-categories, dilations, quantum channels, von Neumann algebras 
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     title = {CP^\ensuremath{\infty} and beyond: 2-categorical dilation theory},
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Robert Allen; Dominic Verdon. CP^∞ and beyond: 2-categorical dilation theory. Theory and applications of categories, Tome 41 (2024), pp. 1783-1811. http://geodesic.mathdoc.fr/item/TAC_2024_41_a49/