Comparison of nonclassical properties resulting from non-Gaussian operations

Based on an asymmetrical beam splitter (ABS) and conditional measurement, we have investigated the nonclassical properties of non-Gaussian slates in a unified form, including photon subtraction, photon addition and quantum catalysis, by deriving analytical expressions for photon number, squeezing effect, Mandel Q parameter and Wigner function. It is found that these properties not only depend on squeezing parameter and measurement, but also on the transmissivity of the ABS. Photon addition and quantum catalysis present a higher probability in the regions of low and high transmissivity, respectively. Although both single-photon subtraction and addition share a dear negative volume, the latter is considered to be a better choice for producing nonclassical states than the two others, if both success probability and negative volume in the small squeezing region are taken into consideration. Quantum catalysis is better in the large squeezing region and with low transmissivity. These results provide some reference for generating such non-Gaussian states.