Detecting nonclassicality and non-Gaussianity by the Wigner function and quantum teleportation in photon-added-and-subtracted two modes pair coherent state

We introduce a new state called photon-added-and-subtracted two modes pair coherent state (PAASTMPCS) by simultaneously adding and subtracting photons to the different modes of a pair coherent state. Its nonclassical and non-Gaussian properties are strengthened by the negative values of its Wigner function as the numbers of photons added or substracted increases. Based on the linear entropy criterion, we indicate that the PAASTMPCS is an entangled state. When increasing the numbers of photons added or substracted to a pair coherent state, the degree of entanglement in the PAASTMPCS is enhanced compared with the original pair coherent state. By using a PAASTMPCS as a non-Gaussian entangled resource, the quantum teleportation process is studied in detail. The results show that the number sum and phase difference measurements protocol is more appropriate than the orthogonal quadrature components measurements protocol in the quantum teleportation process of a coherent state.