2020/06/04 by Roy Araiza, Araiza, Roy, Travis Russell +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Operator Algebras (math.OA) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2006.03094
openalex publication_date 2020/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the set of projections in an operator system can be detected using only the abstract data of the operator system. Specifically, we show that if p is a positive contraction in an operator system V which satisfies certain order-theoretic conditions, then there exists a complete order embedding of V into B(H) mapping p to a projection operator. Moreover, every abstract projection in an operator system V is an honest projection in the C*-envelope of V. Using this characterization, we provide an abstract characterization for operator systems spanned by two commuting families of projection-valued measures and discuss applications in quantum information theory.