In this paper, we investigate the decay behaviors of three imaginarity-related metrics, specifically the $l_1$-norm-based imaginarity measure, imaginarity robustness, and imaginarity relative entropy, for arbitrary single-qubit pure initial states under three typical quantum channels: dephasing, generalized amplitude damping, and phase-amplitude damping. Furthermore, we extend our analysis to higher-dimensional systems by examining the decay trends of the aforementioned imaginarity metrics for several key two-qubit states under two-qubit channels. We also generalize the concept of the maximal imaginary state (originally defined for single qubits in the resource theory of imaginarity) to separable two-qubit states. In addition, we extend the definitions of imaginary power and de-imaginary power for single-qubit channels to two-qubit channels acting on separable two-qubit states. Finally, we compute the imaginary and de-imaginary powers for several common two-qubit channels.

翻译：本文研究了三种与虚性相关的度量——基于$l_1$范数的虚性测度、虚性鲁棒性及虚性相对熵——在三种典型量子信道（退相位信道、广义振幅阻尼信道及相位-振幅阻尼信道）作用下，对任意单量子比特纯初始态的衰减行为。进一步，我们将分析扩展至高维系统，通过考察上述虚性度量在双量子比特信道作用下对若干关键双量子比特态的衰减趋势。同时，我们将最大虚态的概念（最初在虚性资源理论中针对单量子比特定义）推广至可分离的双量子比特态。此外，我们将单量子比特信道的虚化能力与去虚化能力的定义，扩展至作用于可分离双量子比特态的双量子比特信道。最后，我们计算了若干常见双量子比特信道的虚化能力与去虚化能力。