Quantum Information Processing, Vol. 6, No. 6, December 2007 (© 2007)
Can Quantum Information be Processed
by Macroscopic Systems?
Received April 14, 2007; accepted June 29, 2007; Published online: September 5, 2007
We present a quantum-like (QL) model in that contexts (complexes of e.g.
mental, social, biological, economic or even political conditions) are represented
by complex probability amplitudes. This approach gives the possibility to apply
the mathematical quantum formalism to probabilities induced in any domain of
science. In our model quantum randomness appears not as irreducible random-
ness (as it is commonly accepted in conventional quantum mechanics, e.g., by
von Neumann and Dirac), but as a consequence of obtaining incomplete informa-
tion about a system. We pay main attention to the QL description of processing
of incomplete information. Our QL model can be useful in cognitive, social and
political sciences as well as economics and artiﬁcial intelligence. In this paper we
consider in a more detail one special application–QL modeling of brain’s function-
ing. The brain is modeled as a QL-computer.
KEY WORDS: incompleteness of quantum mechanics; quantum-like represen-
tation of information; quantum-like models in biology; psychology; cognitive
and social sciences and economy; context; complex probabilistic amplitude.
PACS: 03.65.-w; 03.67.Lx; 03.67.-a; 87.18.-h.
1. INTRODUCTION: QUANTUM MECHANICS AS OPERATION
WITH INCOMPLETE INFORMATION
Let us assume that, in spite of a rather common opinion, quantum
mechanics is not a complete theory. Thus the wave function does not pro-
vide a complete description of the state of a physical system. Hence we
assume that the viewpoint of Einstein, De Broglie, Schr
Bell, Lamb, Lande, ‘t Hooft and other believers in the possibility to
provide a more detailed description of quantum phenomena is correct,
International Center for Mathematical Modeling in Physics and Cognitive Sciences,
University of V
o, Vaxjo S-35195, Sweden. E-mail: andrei.khrennikov@VXU.se
1570-0755/07/1200-0401/0 © 2007 Springer Science+Business Media, LLC