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

• URL: http://arxiv.org/abs/2210.07732v1
• Date: Fri, 14 Oct 2022 12:03:51 GMT
• Title: The identification of mean quantum potential with Fisher information leads to a strong uncertainty relation
• Authors: Yakov Bloch and Eliahu Cohen
• Abstract summary: The Cramer-Rao bound, satisfied by classical Fisher information, has been shown to give rise to the Heisenberg uncertainty principle of quantum mechanics. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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