General Probabilistic Theories with a Gleason-type Theorem

Victoria J Wright; Stefan Weigert

doi:10.22331/q-2021-11-25-588

General Probabilistic Theories with a Gleason-type Theorem

Victoria J Wright, Stefan Weigert

Mathematics

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

Abstract

Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We identify the class of general probabilistic theories
which also admit Gleason-type theorems. It contains theories satisfying the
no-restriction hypothesis as well as others which can simulate such an unrestricted theory arbitrarily well when allowing for post-selection on measurement outcomes. Our result also implies that the standard no-restriction hypothesis applied to effects is not equivalent to the dual no-restriction hypothesis applied to states which is found to be less restrictive.

Original language	English
Article number	588
Number of pages	34
Journal	Quantum
Volume	5
DOIs	https://doi.org/10.22331/q-2021-11-25-588
Publication status	Published - 25 Nov 2021

Bibliographical note

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10.22331/q-2021-11-25-588Licence: CC BY

General Probabilistic Theories with a Gleason-type Theorem
© The Authors, 2021
Final published version, 927 KBLicence: CC BY

Cite this

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