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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Real-Orthogonal Projections as Quantum Pseudo-Logic
verfasst von : Marjan Matvejchuk, Dominic Widdows
Erschienen in: Quantum Interaction
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Abstract
In the paper, we study linear operators in complex Hilbert space \(\mathbb {C}^n\) that are called real-orthogonal projections, which are a generalization of standard (complex) orthogonal projections but for which only the real part of the scalar product vanishes. We compare some partial order properties of orthogonal and of real-orthogonal projections. In particular, this leads to the observation that a natural analogue of the ordering relationship defined on standard orthogonal projections leads to a non-transitive relationship between real-orthogonal projections. We prove that the set of all real-orthogonal projections in a finite-dimensional complex space is a quantum pseudo-logic, and briefly consider some potential applications of such a structure.