The Identification of Mean Quantum Potential with Fisher Information Leads to a Strong Uncertainty Relation

Yakov Bloch, Eliahu Cohen

Research output: Contribution to journalArticlepeer-review


The Cramér–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 Cramér–Rao bound, to an uncertainty principle which is stronger, in general, than both Heisenberg and Robertson–Schrödinger uncertainty relations, allowing to experimentally test the validity of such an identification.

Original languageEnglish
Article number117
JournalFoundations of Physics
Issue number6
StatePublished - Dec 2022

Bibliographical note

Funding Information:
This research was supported by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation. E.C. was supported by the Israeli Innovation Authority under Projects No. 70002 and No. 73795, by the Pazy Foundation, by ELTA Systems LTD—Israel Aerospace Industries (IAI) division, by the Israeli Ministry of Science and Technology, and by the Quantum Science and Technology Program of the Israeli Council of Higher Education.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.


  • Fisher information
  • Madelung
  • Quantum potential
  • Quantum uncertainty
  • de Broglie-Bohm theory


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