General Probabilistic Theories with a Gleason-type Theorem

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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Cited by in corpus (2)

• Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality
• Intermediate determinism in general probabilistic theories