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Any modification of the Born rule leads to a violation of the purification and local tomography principles

Galley, TD; Masanes, L; (2018) Any modification of the Born rule leads to a violation of the purification and local tomography principles. Quantum , 2 , Article 104. 10.22331/q-2018-11-06-104. Green open access

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Abstract

Using the existing classification of all alternatives to the measurement postulates of quantum theory we study the properties of bi-partite systems in these alternative theories. We prove that in all these theories the purification principle is violated, meaning that some mixed states are not the reduction of a pure state in a larger system. This allows us to derive the measurement postulates of quantum theory from the structure of pure states and reversible dynamics, and the requirement that the purification principle holds. The violation of the purification principle implies that there is some irreducible classicality in these theories, which appears like an important clue for the problem of deriving the Born rule within the many-worlds interpretation. We also prove that in all such modifications the task of state tomography with local measurements is impossible, and present a simple toy theory displaying all these exotic non-quantum phenomena. This toy model shows that, contrarily to previous claims, it is possible to modify the Born rule without violating the no-signalling principle. Finally, we argue that the quantum measurement postulates are the most non-classical amongst all alternatives.

Type: Article
Title: Any modification of the Born rule leads to a violation of the purification and local tomography principles
Open access status: An open access version is available from UCL Discovery
DOI: 10.22331/q-2018-11-06-104
Publisher version: http://dx.doi.org/10.22331/q-2018-11-06-104
Language: English
Additional information: This article is published under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Arts and Sciences (BASc)
URI: https://discovery.ucl.ac.uk/id/eprint/10077773
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