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Identifying weak values with intrinsic dynamical properties in modal theories

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journal contribution
posted on 08.10.2021, 14:35 by Devashish Pandey, Rui Sampaio, Tapio Ala-NissilaTapio Ala-Nissila, Guillermo Albareda, Xavier Oriols
The so-called eigenvalue-eigenstate link states that no property can be associated to a quantum system unless it is in an eigenstate of the corresponding operator. This precludes the assignation of properties to unmeasured quantum systems in general. This arbitrary limitation of orthodox quantum mechanics generates many puzzling situations such as for example the impossibility to uniquely define a work distribution, an essential building block of quantum thermodynamics. Alternatively, modal theories (e.g., Bohmian mechanics) provide an ontology that always allows one to define intrinsic properties, i.e., properties of quantum systems that are detached from any possible measuring context. We prove here that Aharonov, Albert, and Vaidman's notion of a weak value can always be identified with an intrinsic dynamical property of a quantum system defined in a certain modal theory. Furthermore, the fact that weak values are experimentally accessible (as an ensemble average of weak measurements which are postselected by a strong measurement) strengthens the idea that understanding the intrinsic (unperturbed) dynamics of quantum systems is possible and useful in a given modal theory. As examples of the physical soundness of these intrinsic properties, we discuss three intrinsic Bohmian properties, viz., the dwell time, the work distribution, and the quantum noise at high frequencies.

Funding

Spain’s Ministerio de Ciencia, Innovación y Universidades under Grant No. RTI2018-097876-B-C21 (MCIU/AEI/FEDER, UE)

Generalitat de Catalunya and FEDER for the project QUANTUMCAT 001-P-001644

European Union’s Horizon 2020 research and innovation programme under Grant Agreement No, 881603 GrapheneCore3

Marie Skodowska-Curie Grant Agreement No, 765426 (TeraApps)

European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 752822

Spanish Ministerio de Economía y Competitividad (Project No. CTQ2016-76423-P)

Generalitat de Catalunya (Project No. 2017 SGR 348)

Academy of Finland through its QFT Center of Excellence Program grant (No. 312298)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physical Review A

Volume

103

Issue

5

Publisher

American Physical Society (APS)

Version

AM (Accepted Manuscript)

Rights holder

© American Physical Society

Publisher statement

This paper was accepted for publication in the journal Physical Review A and the definitive published version is available at https://doi.org/10.1103/physreva.103.052219.

Acceptance date

14/05/2021

Publication date

2021-05-28

Copyright date

2021

ISSN

2469-9926

eISSN

2469-9934

Language

en

Depositor

Prof Tapio Ala-Nissila. Deposit date: 7 October 2021

Article number

052219