On Consistency of the Quantum-Like Representation Algorithm |
| |
Authors: | Peter Nyman |
| |
Institution: | 1.International Center for Mathematical Modelling in Physics and Cognitive Sciences,University of V?xj?,V?xj?,Sweden |
| |
Abstract: | In this paper we continue to study so-called “inverse Born’s rule problem”: to construct a representation of probabilistic
data of any origin by a complex probability amplitude which matches Born’s rule. The corresponding algorithm—quantum-like
representation algorithm (QLRA)—was recently proposed by A. Khrennikov (Found. Phys. 35(10):1655–1693, 2005; Physica E 29:226–236, 2005; Dokl. Akad. Nauk 404(1):33–36, 2005; J. Math. Phys. 46(6):062111–062124, 2005; Europhys. Lett. 69(5):678–684, 2005). Formally QLRA depends on the order of conditioning. For two observables (of any origin, e.g., physical or biological) a and b, b|a- and a|b conditional probabilities produce two representations, say in Hilbert spaces H
b|a
and H
a|b
. In this paper we prove that under “natural assumptions” (which hold, e.g., for quantum observables represented by operators
with nondegenerate spectra) these two representations are unitary equivalent. This result proves the consistency of QLRA. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|