Nijmegen Quantum Logic Group

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Towards a quantum domain theory: Order-enrichment and fixpoints in W*-algebras

29 Oct 2014 [ proceedings (MFPS) ]

We discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.

From a computer scientist point of view, we explain some fundamental results of operator theory and their relevance in the context of domain theory. In particular, we consider the category W* of W*-algebras together with normal sub-unital maps, provide an order-enrichment for this category and exhibit a class of its endofunctors with a canonical fixpoint.