Geometric stability of expectation regions under Aluthge-type quantum channels

Authors

• Joohyung Kiem, Wonkwang University
• Jaewoong Kim, Korea Military Academy
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

10-2026

Abstract

In quantum theory the quantum expectation region of an observable describes the set of attainable measurement statistics over all pure states. We study how these regions and their maximal expectation values evolve under Aluthge-type quantum channels acting on bounded operators and commuting pairs of operators. These quantum channels generate nonlinear operator flows that regularize non-normal operators while preserving essential measurement information. These results provide a geometric setting for understanding the stability of measurement statistics of compatible quantum operators under structured quantum channels. For a commuting pair𝐓=(𝑇1,𝑇2), we analyze the associated linear pencil   𝐿⁢𝑝⁡(𝐓)={𝑇1+𝜆⁢𝑇2:𝜆∈ℂ},   which admits both generalized and spherical Aluthge quantum channels. We characterize when these quantum channels coincide in terms of the abelian𝐶∗-algebra generated by the corresponding positive operator and interpret this situation as a fixed-point configuration of the induced quantum channels. As a special case, the mean quantum channel yields characterizations of quasinormal operators via matricial quasinormality and stability of quantum expectation regions. Under a convexity stability assumption, we show that the limit of joint quantum expectation regions of iterated spherical Aluthge quantum channels coincides with the convex hull of the Taylor spectrum. We further determine the Taylor spectrum for a pair of the form𝐓=(𝑆,𝛥1⁡(𝑆)) under the Bézout identity and establish a mapping theorem for quantum expectation regions of linear pencils together with inequalities relating joint and pencil maximal expectation values.

Comments

Original published version available at https://doi.org/10.1016/j.aop.2026.170624

Recommended Citation

Kiem, Joohyung, Jaewoong Kim, and Jasang Yoon. "Geometric stability of expectation regions under Aluthge-type quantum channels." Annals of Physics 493 (2026): 170624. https://doi.org/10.1016/j.aop.2026.170624

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Publication Title

Annals of Physics

DOI

10.1016/j.aop.2026.170624