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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具有格里森式定理的一般概率理论

量子理论的格里森式定理允许人们通过假设 (i) 状态一致地为测量结果分配概率，并且 (ii) 每个这样的分配都有一个独特的状态来恢复量子状态空间。我们确定了一类也承认格里森式定理的一般概率理论。它包含满足无限制假设的理论以及其他可以在允许对测量结果进行后选择时任意模拟这种无限制理论的理论。我们的结果还暗示，应用于效果的标准无限制假设并不等同于应用于限制较少的状态的双重无限制假设。