Projection, Entanglement and Nonlocality of Photon-Number Entangled States Generated in Kerr Media

Motivated by the proposal for quantification of Bell nonlocality Phys. Rev. A 92, 030101 (2015), and the concept of ICPS symmetric states Phys. Rev. A 95, 042333 (2017), we present applications of those tools in the case of the physical system, namely photon-number entangled states generated in Kerr media with optical parametric pumping Prog. Opt. 41, 361 (2000). We start from the projection of a density matrix of the considered physical system to the family of ICPS states. For each step of the considered time evolution, we subsequently calculate both the negativity and negativity of projections to examine the lower bound of entanglement versus the actual one. Then we use those projections to calculate the lower bound of nonlocality for the volume of violation.