Gleason-Busch theorem for sequential measurements

Flatt, K., Barnett, S. M. and Croke, S. (2017) Gleason-Busch theorem for sequential measurements. Physical Review A: Atomic, Molecular and Optical Physics, 96(6), 062125. (doi:10.1103/PhysRevA.96.062125)

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Abstract

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957)]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003)], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

Item Type:Articles
Additional Information:This work was supported by the UK Engineering and Physical Sciences Research Council and by the Royal Society (RP150122).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Barnett, Professor Stephen and Flatt, Kieran and Croke, Dr Sarah
Authors: Flatt, K., Barnett, S. M., and Croke, S.
College/School:College of Science and Engineering > School of Physics and Astronomy
Journal Name:Physical Review A: Atomic, Molecular and Optical Physics
Publisher:American Physical Society
ISSN:1050-2947
ISSN (Online):1094-1622
Published Online:20 December 2017
Copyright Holders:Copyright © 2017 American Physical Society
First Published:First published in Physical Review A: Atomic, Molecular and Optical Physics 96(6): 062125
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
721291Astronomy and physics, theoretical physics and application physics / Quantum Theory. Royal Society Research Professorship.Stephen BarnettThe Royal Society (ROYSOC)RP150122S&E P&A - PHYSICS & ASTRONOMY