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Local tomography and the role of the complex numbers in quantum mechanics

Niestegge, Gerd (2020) Local tomography and the role of the complex numbers in quantum mechanics. Proc. R. Soc. A. 476:20200063.

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Abstract

Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown that this can be achieved by postulating that there is a locally tomographic model for a composite system consisting of two copies of the same system. Local tomography is a feature of classical probability theory and quantum mechanics; it means that state tomography for a multipartite system can be performed by simultaneous measurements in all subsystems. The quantum logical definition of local tomography is sufficient, but it is less restrictive than the prevalent definition in the literature and involves some subtleties concerning the so-called spin factors.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Niestegge, Gerdgerd.niestegge@web.de0000-0002-3405-9356
Keywords: Local tomography; Jordan algebra; quantum logic
Subjects: Specific Sciences > Physics > Quantum Mechanics
Depositing User: Dr. Gerd Niestegge
Date Deposited: 18 Jun 2020 02:59
Last Modified: 18 Jun 2020 02:59
Item ID: 17344
Journal or Publication Title: Proc. R. Soc. A. 476:20200063
DOI or Unique Handle: 10.1098/rspa.2020.0063
Subjects: Specific Sciences > Physics > Quantum Mechanics
Date: June 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17344

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