The identification of mean quantum potential with Fisher information leads to a strong uncertainty relation

Abstract

The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show that the identification of the mean quantum potential, an important notion in Bohmian mechanics, with the Fisher information, leads, through the Cramer-Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson-Schrodinger uncertainty relations, allowing to experimentally test the validity of such an identification.

arXiv comment7 pages, accepted to Foundations of Physics as part of a special issue on "Pilot-wave and beyond: Louis de Broglie and David Bohm's quest for a quantum ontology" edited by Aurelien Drezet

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