Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00569020" target="_blank" >RIV/61389005:_____/23:00569020 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1088/1751-8121/acb518" target="_blank" >https://doi.org/10.1088/1751-8121/acb518</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/acb518" target="_blank" >10.1088/1751-8121/acb518</a>

Result language

angličtina

Original language name

Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'

Original language description

In Alase et al (2022 J. Phys. A: Math. Theor. 55 244003), Alase et al wrote that 'the constraint of quasi-Hermiticity on observables' is not 'sufficient to extend the standard quantum theory' because 'such a system is equivalent to a standard quantum system.' Three addenda elucidating the current state of the art are found necessary. The first one concerns the project: in the related literature the original 'aim of extending standard quantum theory' has already been abandoned shortly after its formulation. The second comment concerns the method, viz., the study in 'the framework of general probabilistic theories' (GPT). It is noticed that a few other, mathematically consistent GPT-like theories are available. The authors do not mention, in particular, the progress achieved, under the quasi-Hermiticity constraint, in the approach using the effect algebras. We add that this approach already found its advanced realistic applications in the quasi-Hermitian models using the unbounded operators of observables acting in the infinite-dimensional Hilbert spaces. Thirdly, the 'intriguing open question' about 'what possible constraints, if any, could lead to such a meaningful extension' (in the future) is given an immediate tentative answer: the possibility is advocated that the desirable constraint could really be just the quasi-Hermiticity of the observables, provided only that one has in mind its recently developed non-stationary version.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Volume of the periodical

56

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

7

Pages from-to

038001

UT code for WoS article

000924048500001

EID of the result in the Scopus database

2-s2.0-85147411957