Fock States in Additive Gaussian Noise Channels: Analytical and Numerical Considerations

In this paper, we study the effects of additive Gaussian noise on Fock states. We put forth a simple analytical formula for the resulting output states. Additionally, we conduct numerical analysis into several key properties of noisy Fock states, including their purity, nonclassicality and non-Gaussianness, with respect to the noise parameter. Finally, we examine the impact of noise on entangled N00N states, focusing on its entanglement-breaking effects, which we quantify using the logarithmic negativity measure. Regarding purity, we observe that for a fixed noise level, the purity of a noisy Fock state decreases as the number of photons increases. In terms of non-Gaussianity, we show that at any given noise level, higher Fock states exhibit higher non-Gaussianity compared to lower ones. Although all noisy Fock states eventually lose their nonclassical characteristics under sufficient noise, higher Fock states exhibit more pronounced nonclassical features in low-noise conditions, whereas lower Fock states show greater nonclassicality in high-noise environments. We quantitatively show that the $|2002〉$ state is the most robust against additive Gaussian noise among the N00N states.