Generation of macroscopic entangled states by means of $\chi^{(2)}$ nonlinearity without photon number resolving detection

We generalise the scheme of conditional preparation of $\chi^{(2)}$ macroscopic entangled states [S.A. Podoshvedov, JETP 129, (2006)]. The studied system consists of the system of coupled down converters with type-I phase matching pumped simultaneously by powerful optical fields in coherent states, one auxiliary photon in superposition state of two input modes and projective measurement system. The projective measurement system involves two Hadamard gates introduced to generated output modes followed by photodetectors. Identification of macroscopic entangled states is produced by registration of one photon. No photon number resolving detection is requested for the studied scheme.