Non-positiveWigner Function and Non-Gaussianty Generated by Multiple Creation-then-annihilation Coherent State

We investigate the nonclassicality of a kind of quantum state (MPCACS) generated by repeatedly operating creation-then-annihilation (CA) on the coherent state (CS). Its normalization factor is arduously derived in compact expression related to the Laguerre-polynomial. We explore two observable nonclassical properties of MPCACS, such as non-positive Wigner function and non-Guassianty, which exhibit their highly nonclassical behaviors depending on m . Here, we adopt the Hilbert-Schmidt distance to quantify its Non-Gaussian characters.