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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

56

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

7

Strana od-do

038001

Kód UT WoS článku

000924048500001

EID výsledku v databázi Scopus

2-s2.0-85147411957