Revisited Quantification of the Resource Theory of Imaginarity
This work addresses the quantification of imaginarity in quantum resource theory, offering incremental extensions to higher dimensions for researchers in quantum information.
The paper investigates the decay of three imaginarity metrics for single-qubit and two-qubit states under various quantum channels, and extends concepts like maximal imaginary states and channel powers to higher-dimensional systems, with specific calculations provided for common two-qubit channels.
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.