Quantum non-Gaussianity based on amplified photon statistics

Abstract: Amplification is an essential part of quantum processing and detection that allows for reducing subsequent loss and noise. However, the intensive amplification transfers individual discrete quanta to a detected continuous signal, so Fock probabilities of the unknown input state are not readily available. To solve this issue, we directly derive and analyze a quantum non-Gaussianity witness based on the photon number mean and variance (or alternatively, the second-order correlation $g^{(2)}$) of the unknown state, which can be inferred from post-amplification integrated intensity moments. Since this new witness is based on first and second moments only, measurement results are easy to correct for losses and additive noise.