Coherence dynamics induced by attenuation and amplification Gaussian channels

TL;DR

This paper analyzes how attenuation and amplification Gaussian channels affect the coherence of input Gaussian states, deriving explicit formulas and exploring coherence revival, asymptotic behavior, and entropy production, with implications for quantum thermodynamics.

Contribution

It provides explicit expressions for coherence dynamics under attenuation and amplification channels, including coherence revival and entropy control, advancing understanding of quantum noise effects on Gaussian states.

Findings

Coherence revives with transmissivity in attenuation channels

Coherence reaches asymptotic values in amplification channels

Entropy production can be minimized by parameter control

Abstract

Quantum Gaussian channels play a key role in quantum information theory. In particular, the attenuation and amplification channels are useful to describe noise and decoherence effects on continuous variables systems. They are directly associated to the beam splitter and two-mode squeezing operations, which have operational relevance in quantum protocols with bosonic models. An important property of these channels is that they are Gaussian completely positive maps and the action on a general input state depends on the parameters characterizing the channels. In this work, we study the coherence dynamics introduced by these channels on input Gaussian states. We derive explicit expressions for the coherence depending on the parameters describing the channels. By assuming a displaced thermal state with initial coherence as input state, for the attenuation case it is observed a revival of the coherence as a function of the transmissivity coefficient, whereas for the amplification channel the coherence reaches asymptotic values depending on the gain coefficient. Further, we obtain the entropy production for these class of operations, showing that it can be reduced by controlling the parameters involved. We write a simple expression for computing the entropy production due to the coherence for both channels. This can be useful to simulate many processes in quantum thermodynamics, as finite-time driving on bosonic modes.