2020/05/31 by Victoria J Wright, Stefan Weigert · 1 citation
Arts and Humanities · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Discrete mathematics #Mathematical economics #Mathematics #Philosophy and History of Science #Probabilistic logic #Pure mathematics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Space (punctuation) #State (computer science) #State space #Statistics #Type (biology) #quant-ph
paper · pdf · doi:10.22331/q-2021-11-25-588
published in Quantum 5, 588 (Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften)
arxiv created 2021/11/22 · openalex publication_date 2021/11/25 · arxiv updated 2021/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.