A new fidelity of quantum channel evolution and its geometric interpretation

• URL: http://arxiv.org/abs/2412.03444v1
• Date: Wed, 04 Dec 2024 16:32:59 GMT
• Title: A new fidelity of quantum channel evolution and its geometric interpretation
• Authors: Xiaojing Yan, Xiao Sun, Mingming Du, Jiashan Tang,
• Abstract summary: We define an $alpha$-$z$-fidelity as a significant quantity in quantum information theory. We propose a limit formula for the maximum and the minimum of the fidelity. We offer a geometric interpretation for measuring the distance between quantum states.
• Score: 2.7381317964853737
• License:
• 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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