Revisited Quantification of the Resource Theory of Imaginarity

TL;DR

This paper analyzes how various imaginarity measures decay under different quantum channels for single and two-qubit states, extending the resource theory of imaginarity to higher dimensions and more complex states.

Contribution

It introduces extensions of the resource theory of imaginarity to two-qubit states and channels, including new definitions and decay analyses for these systems.

Findings

Imaginarity measures decay behaviors characterized under multiple quantum channels.

Extended the concept of maximal imaginary states to separable two-qubit states.

Computed imaginary and de-imaginary powers for common two-qubit channels.

Abstract

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.