München 2009 – wissenschaftliches Programm

Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 1: Quanten- Information, Komplexität

MP 1.1: Vortrag

Montag, 9. März 2009, 17:15–17:35, M010

Tensor norms of operator systems and Tsirelson’s problem — •Volkher Scholz and Reinhard F. Werner — Technical University of Braunschweig

We discuss some possible ambiguities in the definition of “correlations produced by quantum systems”, which were noted by Acin [M. Navascues, S. Pironio and A. Acin, Bounding the set of quantum correlations, Phys. Rev. Lett 98, 010401 (2007)] and formulated in a sharp way by Tsirelson [B.S. Tsirelson, Bell inequalities and operator algebras, Problem 33 on the Braunschweig list, http://www.imaph.tu-bs.de/qi/problems/33.html]. The issue is the notion of “subsystem”, or the kind of independence postulated between two observers Alice and Bob. If we just assume that all of Alice’s observables commute with all of Bob’s, we might get some larger set of correlations than if we assume in addition that these commuting observables act on different tensor factors in a tensor product decomposition of the underlying Hilbert space.

Tsirelson showed already that if the ambient Hilbert space is finite dimensional, this distinction is irrelevant. The problem of Tsirelson is to decide the question in case of arbitrary Hilbert spaces and observable algebras. We show here that the problem is equivalent to the question whether all quantum correlations can be approximated by correlations between finite dimensional systems. Although we do not offer a solution, we do link the problem to issues well-known in the theory of C*-algebras, von Neumann algebras and operator systems.