  We consider a family of continuous variable (CV) states being a superposition
of displaced number states with equal modulo but opposite in sign displacement
amplitudes. Either an even or odd CV state is mixed with a delocalized photon
at a beam splitter with arbitrary transmittance and reflectance coefficients
with the subsequent registration of the measurement outcome in an auxiliary
mode to deterministically generate hybrid entanglement. We show that at certain
values of the experimental parameters maximally entangled states are generated.
The considered approach is also applicable to truncated finite versions of
even/odd CV states. We study the nonclassical properties of the introduced
states and show their Wigner functions exhibit properties inherent to
nonclassical states. Other nonclassical properties of the states under
consideration have also been studied.
