Basic Quantum Theory and the Necessity for Its Revision

Basil S. Davis

Максим Евгеньевич Широков

Abstract A revised version of the compactness criterion for families of quantum operations in the strong convergence topology obtained in [1] is presented, along with a more detailed proof and the examples showing the necessity of this revision. Several criteria for the existence of limit points of a sequence of quantum operations w.r.t. the strong convergence are obtained and discussed. Applications in different areas of quantum information theory are described.

G. Gouesbet

There is a huge number of laments concerning the lack of intelligibility of quantum mechanics. Some ingredients of quantum mechanics may however be possibly understood by referring to first principles, that is to say to basic principles (or postulates) which are clear and distinct to the intuition. In particular, if we rely on a first principle called non-singularity principle, which may be viewed as a hypothesis, we claim that quantum mechanics can be viewed as the a priori consequence of a rational demand. The status of the non-singularity principle, obvious to most physicists, may however be criticized, on the basis that there is no universal intuition and that any statement is in principle revisable.

Jean-Marc Lévy-Leblond

L.D. Faddeev, L.A. Khalfin, I.V. Komarov

The subject of my talk is the relations between the mathematical theory of extremal problems and the physical theory of quanta.1 The theory of quanta, or quantum mechanics, studies phenomena in the world of bodies of atomic scale. It turned out that the usual notions of motion and the usual methods of description of a mechanical system were inapplicable for such bodies. One needed to find another formulation of the basic laws of nature instead of the old one based on observations of bodies containing a very large number of atoms. The drastic revision of all usual notions of mathematics and physics was required. As a result of this revision and due to the efforts of several scientists such formulation has been found and the theory, which is as elegant and complete as the Newton mechanics is, has been created. This new theory — the new quantum mechanics — contains the Newton mechanics as a limiting case. Although some particular questions and problems remain open, the basic principles and the mathematical technique of the new theory can be considered to be completely established.