Quantum Collections

Andre Kornell

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arXiv · 1202.2994

Quantum Collections

Andre Kornell

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Abstract

We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-algebras, we construct their free exponential, which in the context of this analogy corresponds to the collection of functions from one of these W*-algebras to the other. We also show that every unital normal completely positive map between W*-algebras arises naturally from a normal state on their free exponential.

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Andre Kornell. 2012-02-14. Quantum Collections. https://arxiv.org/abs/1202.2994

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