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

0569020 - ÚJF 2024 RIV GB eng J - Journal Article
Znojil, Miloslav
Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory'.
Journal of Physics A-Mathematical and Theoretical. Roč. 56, č. 3 (2023), č. článku 038001. ISSN 1751-8113. E-ISSN 1751-8121
Institutional support: RVO:61389005
Keywords : PT symmetry * quasi-Hermiticity * effect algebras
OECD category: Applied mathematics
Impact factor: 2.1, year: 2022
Method of publishing: Open access
https://doi.org/10.1088/1751-8121/acb518

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.
Permanent Link: https://hdl.handle.net/11104/0340301