Noncollinear biphoton states: enormously high resource of azimuthal entanglement as it's seen in Cartesian variables

Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of Spontaneous Parametric Down-Conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high and, in fact, this is the same enormous resource of azimuthal entanglement which was found to occur in the formalism of spherical angles used for characterization of photon wave vectors (Phys. Rev. A, {\bf 93}, 033830, 2016). In Cartesian variables this phenomenon manifests itself as a strong broadening and a very unusual and peculiar shape of the arising single-particle distribution curves. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental scheme this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.