A new fidelity of quantum channel evolution and its geometric interpretation

Fuente: arXiv
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Auteurs principaux: Yan, Xiaojing, Sun, Xiao, Du, Mingming, Tang, Jiashan
Format: Preprint
Publié: 2024
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author Yan, Xiaojing
Sun, Xiao
Du, Mingming
Tang, Jiashan
author_facet Yan, Xiaojing
Sun, Xiao
Du, Mingming
Tang, Jiashan
contents 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 $α$-$z$-fidelity as a significant quantity in quantum information theory and give the properties of the fidelity with orders $α$ and $z$. Secondly, by analyzing the $α$-$z$-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 $α$-$z$-fidelity. In addition, we have extended the $α$-$z$-Rényi 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_03444
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A new fidelity of quantum channel evolution and its geometric interpretation
Yan, Xiaojing
Sun, Xiao
Du, Mingming
Tang, Jiashan
Quantum Physics
81P47
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 $α$-$z$-fidelity as a significant quantity in quantum information theory and give the properties of the fidelity with orders $α$ and $z$. Secondly, by analyzing the $α$-$z$-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 $α$-$z$-fidelity. In addition, we have extended the $α$-$z$-Rényi 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.
title A new fidelity of quantum channel evolution and its geometric interpretation
topic Quantum Physics
81P47
url https://arxiv.org/abs/2412.03444