Quantum Interaction

A detailed study of quantum correlations reveals that reconstructions based on physical principles often fail to reproduce the quantum bound in the general case of N -partite correlations. We read here an indication that the notion of system, implicitly assumed in the operational approaches, becomes problematic. Our approach addresses this issue using algebraic coding theory. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing ‘bipartite systems,’ we find strong evidence of an upper bound on bipartite correlations equal to 2.82537, which is measurably lower than the Tsirelson bound. 1 Mathematics Guides Understanding A large swath of new research in the foundations of quantum theory addresses the problem of correlations between distant parties. It had been known since the “second quantum revolution” started by John Bell [3] that the amount of correlations is a decisive quantity distinguishing between local (classical) and nonlocal physical theories. However, it was only noticed quite recently that the amount of correlations or, more broadly, quantum bounds in Bell inequalities are, by themselves, a formidable puzzle through which, once we are able to understand it better, we may get an entirely new understanding of quantum theory. Quantum logical reconstructions have reached their peak when George Mackey and, later, Constantin Piron gave examples of mathematical derivations of the Hilbert space formalism from an orthomodular lattice with additional assumptions [18,26]. After a decline of two decades, operational reconstructions of quantum theory took over from quantum logic around the turn of the century. Finite-dimensional Hilbert spaces came into focus of these reconstructions as a result of the development of quantum information. To derive the Hilbert space, one posits several physical principles that are given a mathematical formulation with the operation framework [5,15,22]. Such reconstructions contain an important insight: an assumption of continuity is a necessary, but not a sufficient, ingredient of quantum mechanical axiomatic systems. Differently worded continuity assumptions exist in every reconstruction [16,32]: a prominent representative is the existence of a continuous reversible transformation between any c © Springer International Publishing Switzerland 2016 H. Atmanspacher et al. (Eds.): QI 2015, LNCS 9535, pp. 3–11, 2016. DOI: 10.1007/978-3-319-28675-4 1