By virtue of the technique of integration within an ordered product (IWOP) of operators and the bipartite entangled state representation, we derive some new identities about operator Hermite polynomials in both the single-and two-variable cases. We also find a binomial-like theorem between the single-variable Hermite polynomials and the two-variable Hermite polynomials. Application of these identities in deriving new integration formulas, but without really doing the integration in the usual sense, is demonstrated.
We propose a simple scheme to generate x-type four-charge entangled states by using SQUID-based charge qubits capacitively coupled to a transmission line resonator （TLR）. The coupling between the superconducting qubit and the TLR can be effectively controlled by properly adjusting the control parameters of the charge qubit. The experimental feasibility of our scheme is also shown.
