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# Supplementary information files for: Identifying weak values with intrinsic dynamical properties in modal theories

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posted on 2021-10-08, 15:32 authored by Devashish Pandey, Rui Sampaio, Tapio Ala-NissilaTapio Ala-Nissila, Guillermo Albareda, Xavier OriolsSupplementary files for: Identifying weak values with intrinsic dynamical properties in modal theories.

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