Using macroscopic entanglement to close the detection loophole in Bell inequality

We consider a Bell-like inequality performed using various instances of multi-photon entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the "size" of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more "macroscopic" form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loophole. Differently, losses before the unitary transformations cause decoherence effects that cannot be compensated using macroscroscopic entanglement.