Nonclassicality Of Hermite Polynomial State

Nonclassicality of optical fields has been a topic of great interest in quantumoptics and quantum information processing. The nonclassicality of quantum states canbe characterized by some nonclassical properties such as the antibunching，negativityof the Wigner function (WF), squeezing in one of the phase quadrature components,and sub-Poissonian photon statistics. Among them, the partial negativity of the WF isindeed a good indication of the highly nonclassical character of the state. Therefore itis worth of obtaining the WF for any states and to measure their negative values.In this paper, we sahll investigate the nonclassical properties of Single-variableHermite polynomial state and two-variable Hermite polynomial state with the help ofIWOP technique. The study on these states can not only deepen our understanding ofthe nature of quantum fields, but also help us to realize these fields for possible futureapplications in experiment, such as in weak-signal detection, quantum computing, andquantum coding.