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arXiv · 2412.03444

A new fidelity of quantum channel evolution and its geometric interpretation

Xiaojing Yan·Xiao Sun·Mingming Du·Jiashan Tang
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Abstract

Fidelity is crucial for characterizing transformations of quantum states under various quantum channels, which can be served as a fundamental tool in resource theories. Firstly, we define an $\alpha$-$z$-fidelity as a significant quantity in quantum information theory and give the properties of the fidelity with orders $\alpha$ and $z$. Secondly, by analyzing the $\alpha$-$z$-fidelity under the evolution of different types of quantum channels (single orbit, all quantum channels, unitary quantum channels, and mixed unitary quantum channels), we propose a limit formula for the maximum and the minimum of the $\alpha$-$z$-fidelity. In addition, we have extended the $\alpha$-$z$-R\'enyi relative entropy, providing new insights into its relevance for resource quantification. Finally, we offer a geometric interpretation for measuring the distance between quantum states, contributing to the broader understanding of the operational and transformative power of dynamical quantum resources across various physical settings.

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Xiaojing Yan, Xiao Sun, Mingming Du, Jiashan Tang. 2024-12-04. A new fidelity of quantum channel evolution and its geometric interpretation. https://doi.org/10.1007/s11128-025-04823-5

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