  We show that hybrid local measurements combining homodyne measurements and
photodetection provide violations of a Bell inequality with arbitrarily low
photodetection efficiency. This is shown in two different scenarios: when one
part receives an atom entangled to the field mode to be measured by the other
part and when both parts make similar photonic measurements. Our findings
promote the hybrid measurement scenario as a candidate for loophole-free Bell
tests beyond previous expectations.
