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Beyond Purity and Mixtures in Categorical Quantum Mechanics

de Ronde, Christian and Massri, Cesar (2020) Beyond Purity and Mixtures in Categorical Quantum Mechanics. [Preprint]

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Abstract

In a recent paper [12], we discussed the serious inconsistency present within the operational and mathematical definition(s) of the notion of pure state. Continuing this analysis, in this work we attempt to address the role of ‘purity’ and ‘mixtures’ within two different categorical approaches to QM, namely, the topos approach originally presented by Chris Isham and Jeremy Butterfield [27, 28, 29] and the more recent logos categorical approach presented by the authors of this article [10, 11, 13]. While the first approach exposes the difficulties to produce a consistent understanding of pure states and mixtures, the latter approach presents a new scheme in which their reference is erased right from the start in favor of an intensive understanding of projection operators and quantum superpositions. This new account of the theory, grounded on an intensive interpretation of the Born rule, allows us not only to avoid the orthodox interpretation of projection operators —either as referring to definite valued properties or measurement outcomes— but also to consider all matrices (of any rank) on equal footing. It is from this latter standpoint that we conclude that instead of distinguishing between pure and mixed states it would be recommendable —for a proper understanding of the theory of quanta— to return to the original matrix formulation of quantum mechanics presented by Werner Heisenberg in 1925.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
de Ronde, Christiancderonde@gmail.com
Massri, Cesar
Keywords: pure state, mixture, quantum mechanics, graphs.
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Christian de Ronde
Date Deposited: 11 Feb 2020 00:40
Last Modified: 11 Feb 2020 00:40
Item ID: 16903
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: 10 February 2020
URI: http://philsci-archive.pitt.edu/id/eprint/16903

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