Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum Articles uri icon

publication date

  • March 2018

volume

  • 25

International Standard Serial Number (ISSN)

  • 1230-1612

abstract

  • The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon's entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical sub-manifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

keywords

  • information geometry; statistical models; quantum mechanics.