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

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Abstract

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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan, 5290002, Israel

    Yakov Bloch & Eliahu Cohen

  2. Department of Physics, Bar-Ilan University, Ramat Gan, 5290002, Israel

    Yakov Bloch

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  1. Yakov Bloch
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  2. Eliahu Cohen
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Both authors contributed significantly to all aspects of the work.

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Correspondence to Eliahu Cohen.

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Bloch, Y., Cohen, E. The Identification of Mean Quantum Potential with Fisher Information Leads to a Strong Uncertainty Relation. Found Phys 52, 117 (2022). https://doi.org/10.1007/s10701-022-00638-x

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