Beam splitters as controlled-Z gate for hybrid state

We explore a scheme based on adding a nonlocal photon and subtracting some number of photons to entangle the initial single-mode squeezed vacuum (SMSV) state with the photon state. In a realistic model of interaction of the SMSV state with the photonic state on a beam splitter (BS) with changeable transmissivity or reflectivity the hybrid entanglement is realized for any values of the squeezing of input SMSV state. Maximum hybrid entanglement is achieved at certain values of the squeezing and BS parameter, which can mean implementation of a two-qubit controlled-Z (CZ-) operation using the BS with the appropriate initialization of the input states. The success probability of the gate, taking into account multiphoton outcomes in the measuring mode of the BS, is more than 0.3. We also propose to use new continuous variable (CV) states of definite parity that could increase the success probability of generating maximal hybrid entanglement. We show sufficient robustness of the generated entanglement under photon number resolving detection with practical quantum efficiency.