A computer scientist's reconstruction of quantum theory

DOI10.1088/1751-8121/AC8459zbMATH Open1519.81017arXiv2109.10707MaRDI QIDQ6378277

John van de Wetering, Bas Westerbaan

Publication date: 22 September 2021

Abstract: The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure of quantum systems comes from. From a computer scientist's perspective we would like to study quantum theory in a way that allows interesting transformations and compositions of systems and that also includes infinite-dimensional datatypes. Here we present such a compositional reconstruction of quantum theory that includes infinite-dimensional systems. This reconstruction is noteworthy for three reasons: it is only one of a few that includes no restrictions on the dimension of a system; it allows for both classical, quantum, and mixed systems; and it makes no a priori reference to the structure of the real (or complex) numbers. This last point is possible because we frame our results in the language of category theory, specifically the categorical framework of effectus theory.

Mathematics Subject Classification ID

Constructive quantum field theory (81T08) Applications of selfadjoint operator algebras to physics (46L60) Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) (81P10) Operator algebra methods applied to problems in quantum theory (81R15) Categories of spans/cospans, relations, or partial maps (18B10) Quantum state spaces, operational and probabilistic concepts (81P16)

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