General Probabilistic Theories with a Gleason-type Theorem

• URL: http://arxiv.org/abs/2005.14166v4
• Date: Mon, 22 Nov 2021 14:33:00 GMT
• Title: General Probabilistic Theories with a Gleason-type Theorem
• Authors: Victoria J Wright, Stefan Weigert
• Abstract summary: Gleason-type theorems for quantum theory allow one to recover the quantum state space. We identify the class of general probabilistic theories which also admit Gleason-type theorems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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