Real-Orthogonal Projections as Quantum Pseudo-Logic

In the paper, we study linear operators in complex Hilbert space Cn 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 nontransitive 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.

• Type: Journal
• Year: 2015
• Where: QI
• Authors: Marjan Matvejchuk, Dominic Widdows
• Keywords: Physics, QI 2015