Optical spin squeezing: bright beams as high-flux entangled photon sources

In analogy with the spin-squeezing inequality of Wang and Sanders [Physical Review A 68, 012101 (2003)], we find inequalities describing macroscopic polarization correlations that are obeyed by all classical fields, and whose violation implies entanglement of the photons that make up the optical beam. We consider a realistic and exactly-solvable experimental scenario employing polarization- squeezed light from an optical parametric oscillator (OPO) and find that any two photons separated by less than the OPO coherence time are polarization entangled. The polarization entanglement is robust against losses and extremely bright: efficiency can exceed that of existing "ultra-bright" pair sources by at least an order of magnitude. This translation of spin-squeezing inequalities to the optical domain will enable direct tests of the squeezing-entanglement relationship.