Investigation Of Single-Mode Squeezing Operator By Fresnel Operators And Its Application In Quantum Information

Classical optics mainly studies the propagation of light waves in a variety of media, dealing with the spatial distribution function of various light waves, and the integral transformation of these distribution functions. Quantum optics and classical optical research objects are related to the properties of light, but the properties of the light and the mathematical methods used are different.Fan Hongyi and someone else through the symbolic method invented by Dirac made classical optics and quantum optics can produce very good correspondence and found that there are many similarities in the classical optics and quantum optics.First, we show that squeezing mechanism involved in a degenerate parametric amplifier(DPA) actually corresponds to optical Fresnel transformation. We then employ the technique of integration within ordered product(IWOP) of operators to obtain the concrete form squeezed state. In this way, the squeezing mechanism in DPA is discussed in the context of Fresnel operator theory.In addition, we introduce a kind of non-Gaussian quantum state with continuous variable by operating high-order coherent superposition of photon-subtraction on two single-mode squeezed vacuum states. Using the normally ordering form of squeezing operation and completeness relation of coherent state representation, we derive the analytical expression of normalized factor of this new state. It is found that the factor is related to Legendre polynomials. Based on the teleportation scheme of KimbleBraunstein, we calculate the fidelity for teleporting coherent state by using the new entangled state as entangled resource. It is shown that(i) the fidelity has a maximum value when two squeezing parameters are equal;(ii) the fidelity becomes worse than that from the case without coherent superposition operation for odd m; while for even m, the fidelity can be improved in a certain small squeezing parameter region, and even exceeds 1/2. In addition, the fidelity increases as even m in a certain region.