  We develop theory of realization of hybrid entanglement between
discrete-variable (single photon) and continuous-variable states (coherent
states). A highly transmissive beam splitter (HTBS) is used for interaction of
the ingredients. Mechanism for generating the hybrid entangled states is based
on the simultaneous displacement of the discrete-variable state on equal in
absolute value but opposite in sign displacement amplitudes by coherent
components, in such a way that all the information about the displacement
amplitudes is lost with subsequent registration of photons in the auxiliary
mode. Conditions for the balanced hybrid entangled states generation are found.
Our approach follows along lines experimentally demonstrated in Nat. Photonics
8, 570-574 (2014).
