Imaginarity Resource Theory of Gaussian Quantum Channels

TL;DR

This paper introduces new frameworks and measures for quantifying the imaginarity resource in Gaussian quantum channels, providing computationally simple and physically meaningful tools.

Contribution

It proposes two frameworks for imaginarity quantification of Gaussian channels and introduces three measures, including one applied to Quantum Brownian Motion channels.

Findings

I_c^GC measure is fully determined by channel parameters and is continuous.

The measures are computationally tractable and applicable to dynamical processes.

Application to Quantum Brownian Motion channels demonstrates practical utility.

Abstract

Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.