A possible operational motivation for the orthocomplementation in quantum structures (Q618790)

In the foundations of quantum mechanics, Gleason's theorem dictates the uniqueness of the state transition probability. The author argues that the state transition probability could be regarded as a primitive concept instead of being derived from the structure on the set of states and properties. He adopts an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties, and the possible (measurement) contexts (State-Context-Property formalism, SCOP). Two Gleason-like conditions are proved to imply orthocomplementation of the lattice of properties, thus providing a motivation for one of the ``quantum axioms'' used in the Piron-Solèr representation theorem. None of these conditions appears to be necessary.