Quantum
theory as optimal encoding of probabilistic information
Johann Summhammer
Paper presented at International
Conference on Quantum Structures, Vienna, July 1 - 7, 2002
Abstract:
Quantum experiments yield random data. We show that the most efficient way to
store
this empirical information by a finite number of bits is by means of the vector
of square
roots of observed relative frequencies. This vector has the unique property
that its dispersion
becomes invariant of the underlying probabilities, and therefore invariant
of the physical
parameters. This also extends to the
complex square roots, and it remains true under
a unitary transformation effected by a quantum evolution. This reveals quantum
theory
as a statistical theory of making predictions which are as accurate as the
input information,
without
any statistical loss. Our analysis also suggests that from the point of view of
information a slightly more accurate theory than quantum theory should be
possible.
Full paper (PDF, 223k: 14 pages, including 5 figures)
J.Summhammer
Online version available!
J. Summhammer, K.A. Hamacher, H. Kaiser, H. Weinfurter, D.L.Jacobsonand S.A.
Werner
Published in: Phys.Rev.Lett 75, 3206 (1995).
Abstract:
Polarized neutron interferometry has been used to measure the amplitudesforthe
exchange of up to five photons between the neutron and an
oscillatingmagneticfield. The Rabi spin flip configuration and a configuration
in whichspinflip is suppressed were investigated, because they raise
differentquestionson the conservation of angular momentum. Due to the linearity
ofthe time-dependentinterference signal in the exchange amplitudes ,
photonexchangeprobabilities below one percent could be resolved.
J.Summhammer
Published in: Phys.Rev.A 54, 3155 (1996).
Abstract:
For the study of energy quantization in low frequency potentials
andtheaccompanying quantum effects we analyze a silicon double crystal
arrangementexploitingdynamical diffraction of neutrons to achieve the required
extremelyhighenergy resolution. The first crystal prepares a minimumuncertainty
beamwhich passes a potential region whose influence on theneutron energy isanalyzed
by the second crystal. With realistic parameterschanges of neutronenergy below
0.5
G.Krenn, J.Summhammer, K.Svozil
Online version available!
G.Krenn, A.Zeilinger
Online version available!
G.Krenn, K.Svozil
Online version available!
Changes
by J.Summhammer 4.Apr.2003