A Gleason-type theorem for qubits based on mixtures of projective measurements

Stefan Ludwig Otto Weigert; Victoria J Wright

doi:10.1088/1751-8121/aaf93d

A Gleason-type theorem for qubits based on mixtures of projective measurements

Stefan Ludwig Otto Weigert, Victoria J Wright

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of projective measurements and their classical mixtures. This assumption is significantly weaker than those required for existing Gleason-type theorems valid in dimension two.

Original language	English
Article number	055301
Number of pages	19
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	52
Issue number	5
Early online date	18 Dec 2018
DOIs	https://doi.org/10.1088/1751-8121/aaf93d
Publication status	Published - 10 Jan 2019

Bibliographical note

© 2019 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Keywords

quant-ph
Gleason's theorem
postulates of quantum theory
quantum measurement
projective-simulable measurements
frame functions
quantum probability rule

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10.1088/1751-8121/aaf93d

20181210PSMGleasonForQubits(acceptedVs)
© 2019 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 223 KB
1808.08091v1
© 2019 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.
Accepted author manuscript, 274 KBLicence: CC BY-NC-ND

Cite this

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A Gleason-type theorem for qubits based on mixtures of projective measurements

Abstract

Bibliographical note

Keywords

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