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

Editorial Material Physics, Multidisciplinary

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

Miloslav Znojil

Summary: In Alase et al's article, it is argued that the constraint of quasi-Hermiticity on observables is insufficient to extend standard quantum theory, as such a system is equivalent to a standard one. Three important points are raised: the abandoned original aim of extending quantum theory, the existence of other mathematically consistent theories in the framework of general probabilistic theories, and the progress made using effect algebras under the quasi-Hermiticity constraint. They propose that the recently developed non-stationary version of quasi-Hermiticity might provide the desired constraint for a meaningful extension.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2023)

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Article Physics, Multidisciplinary

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

Abhijeet Alase et al.

Summary: This study aims to answer the question of whether there exists a consistent physical theory that extends standard quantum theory with PT-symmetric observables. The study finds that, according to the framework of general probabilistic theories, the resulting theory from imposing PT-symmetry on observables only allows for one trivial state. Moreover, considering the constraint of quasi-Hermiticity on observables, the study shows that such a system is equivalent to a standard quantum system. If all observables are both quasi-Hermitian and PT-symmetric, then the system is equivalent to a real quantum system.

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL (2022)

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Article Physics, Multidisciplinary

Observing a changing Hilbert-space inner product

Salini Karuvade et al.

Summary: In quantum mechanics, physical states are represented by rays in Hilbert space H, which is a vector space with an inner product. The inner product represents the overlap between |psi>, a description of a pure state (preparation), and |psi>.

PHYSICAL REVIEW RESEARCH (2022)

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Article Optics