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arXiv 2006.030942020-06math.OAquant-ph

An abstract characterization for projections in operator systems

Roy Araiza, Travis Russell

备注：: Final version. To appear in Journal of Operator Theory

英文摘要：

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.

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