Significance of fidelity deviation in continuous-variable teleportation

Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in continuous -variable (CV) teleportation, i.e., the fidelity deviation as the figure of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non-Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different input scenarios: One is when input states are sampled from constrained uniform distribution while the other one is Gaussian suppression of the input states which again leads to a different classification of CV states according to their performance. The entire analysis is carried out in noiseless and noisy scenarios with noise being incorporated in the measurement and the shared channels. We also report that one type of noise can make the protocol robust against the other one, which leads to a "constructive effect," and identify the noise models which are responsible for decreasing average fidelity and the increment in fidelity deviation.