Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Immediately after formulation of quantum mechanics there were attempts to “derive” it from some small set of plausible axioms. The two most successful approaches were: algebraic axiomatisation (started by Jordan, von Neumann and Wigner) and so called quantum logic approach, based on the partially ordered structure of “propositions” about physical system (started by Birkhoff and von Neumann). During many years of development the latter approach became mostly the theory of partially ordered structures with a little application in physics.Since 1990s some physicist working on quantum information theory become interested in the so-called no-signalling theories. These are very intuitive, in some sense minimal, models of compound systems. It seemed that such theories are more general than quantum mechanics.Our idea is to rigorously reformulate assumptions of non-signalling theories in the framework of quantum logics and then study its properties and true relation to quantum mechanics.