Controllable shaping of CV–DV entanglement between CV states of certain parity and delocalized photon

Hybrid entangled states are necessary for quantum information processing within heterogeneous quantum networks. We develop an entanglement mechanism between continuous variable (CV) states of definite parity and delocalized photon (discrete variable (DV) state) leading to deterministic generation of the hybrid entangled states. The mechanism is realized by means of mixing of the input states on beam splitter (BS) with arbitrary transmission and reflection coefficients followed by measurement of the number of photons in the measurement mode by photon number resolving (PNR) detector. The scheme under study allows for one to partially control hybrid entanglement by change of the transmission/reflection coefficients of the BS. There are wide domains of values which guarantee the generation of maximum hybrid entanglement. The mechanism of the CV–DV entanglement can be used for controllable entangled state distribution in hybrid optical network.