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

Abstract

An elucidation of the current state of art in quasi-Hermitian quantum theory (QHQT) as inspired by the recent paper by Alase et al (J. Phys. A: Math. Theor. 55 (2022) 244003, paper [1]) is offered. We point out that the author's main discovery (viz., that the QHQT does not extend the standard quantum theory) is not new. In a related comment on the author's method of proof performed in ``the framework of general probabilistic theories'' (GPT) we add that also in this context a few other, mathematically consistent GPT-like theories are already available in the literature (pars pro toto we mention the results using the so called effect algebras). Thirdly, the ``intriguing open question'' about ``what possible constraints, if any, could lead to such a meaningful extension'' is given a tentative answer: The constraint could be just the generalized, non-stationary version of the quasi-Hermiticity.