Micro-macro entanglement and coarse-grained measurements

We are studying the demonstration of entanglement in a micro-macro system. The entanglement is produced via parametric down conversion process between two photons and is being amplified through a phase-co-variant cloner to entanglement between a photon and a beam of light. We introduce an analogous system which exploits an entanglement breaking amplifier and produces only classical correlation between the two parties. We show that it is hard to distinguish the outcomes of the two systems, considering even a small inaccuracy in photon counting measurements. We model these inaccuracies as coarse-graining. The result is that for certain types of measurements, small coarse- graining makes the classical and quantum mechanical correlation indistinguishable.