
Apr 25 2012
Stellenbosch Node Seminar: Prof Howard Barnum (University of New Mexico and STIAS Fellow)
NITheP cordially invites you to a seminar by:
Prof Howard Barnum
University of New Mexico and STIAS Fellow
Date: Wednesday 25th of April 2012
Time: 14:00
Venue: NITheP Stellenbosch Node, Seminar Room
TITLE: A simple characterization of finitedimensional quantum theory and Jordanalgebraic theories
ABSTRACT: We show that the quantum description of finitedimensional systems, in terms of states, measurements, and probabilities of measurement outcomes, is characterized by four simple principles having an informational flavor. This characterization takes place within a much broader framework which conceives of states as effectively catalogues of probabilities for measurement results, and the space of states as an essentially arbitary compact convex set of such probability assignments. The background assumption of finite dimensionality simplifies the mathematics but may well be dispensable.
The first three principles characterize finite dimensional formally real Jordanalgebraic systems. The notion of Jordan algebra was abstracted from properties of the Hermitian operators of quantum theory by Pascual Jordan in 1932, and the finitedimensional ones were completely described by Jordan, von Neumann, and Wigner in 1935. Our characterizing principles can be roughly described as (1) a generalized spectral decomposition, (2) a high degree of symmetry, and
(3) a generalization of the Lüders version of the projection postulate of quantum theory. One then obtains standard complex quantum theory by requiring (4) "local tomography": that the state of a composite system be determinable from the statistics (including correlations) it induces for local observables.
Several principles may be used as alternatives to principle (3); notable examples are (3') the "covering law" of quantum logic as applied to the lattice of faces of the state space, and (3'') the principle that the theory exhibits no interference of higher than second order in R. Sorkin's hierarchy (as adapted in work of two of us (HB and CU) with J. Emerson, to the convex sets framework for theories).
This is joint work with Markus Mueller (Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada) and Cozmin Ududec (University of Waterloo and Perimeter Institute)
Navrae/Enquiries: René Kotzé
Tel: 021 808 2653
Email: renekotze@sun.ac.za
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