A computer scientist's reconstruction of quantum theory*BW: The majority of the work was carried out while employed at University College London and Radboud Universiteit Nijmegen. (23rd September 2022)

• Record Type: Journal Article
• Authors: Westerbaan, Bas; van de Wetering, John
• Is Part Of: Journal of physics. Volume 55:Number 38(2022)
• Publication Date: 2022-09-23
• Subjects: effectus -- reconstruction of quantum theory -- effect algebra -- sequential product -- Jordan algebra -- von Neumann algebra -- JBW-algebra; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac8459
• Languages: English
• ISSNs: 1751-8113

Abstract

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.