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Towards a quantum domain theory: order-enrichment and fixpoints in \(W^*\)-algebras. (English) Zbl 1337.81041

Jacobs, Bart (ed.) et al., Proceedings of the 30th conference on the mathematical foundations of programming semantics (MFPS XXX), Ithaca, NY, USA, June 12–15, 2014. Amsterdam: Elsevier. Electronic Notes in Theoretical Computer Science 308, 289-307, electronic only (2014).
Summary: 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 \(\mathbf{W^*}\) 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.
For the entire collection see [Zbl 1310.68012].

MSC:

81P68 Quantum computation
06B35 Continuous lattices and posets, applications
18D20 Enriched categories (over closed or monoidal categories)
47L90 Applications of operator algebras to the sciences
68Q55 Semantics in the theory of computing

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References:

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