Cohering and decohering power of single-mode Gaussian noises

Quantum coherence stems from the superposition principle of states. It shows an essential feature of quantum systems which is different from the classical phenomena. We investigate the concept of cohering and decohering power of single-mode quantum Gaussian noises. For this purpose, we use the Hellinger distance-based and Bures distance-based measure to quantify the coherence of single-mode quantum Gaussian states. We will show that both Hellinger and Bures distance-based measures are the same when quantifying the quantum coherence of pure single-mode quantum Gaussian states. In this work we will study the cohering and decohering power of single-mode attenuation and amplification noise. We will investigate the effects of the amplification parameter k and attenuation parameter on the cohering and decohering power of corresponding channels. We find that for single-mode amplification noise the cohering power is increased by increasing k, while the decohering power is decreased by increasing k. Conversely, we will see that for a single-mode attenuation channel the cohering power is decreased by increasing the attenuation parameter , while in general the decohering power is increased by increasing . We also investigate the effect of the mean photon number of the environment N on the cohering and decohering power of single-mode attenuation and amplification noises. For both of the channels the cohering power is increased, while the decohering power is decreased, by increasing N.