  We show that the use of probabilistic noiseless amplification in entangled
coherent state-based schemes for the test of quantum non locality provides
substantial advantages. The threshold amplitude to falsify a Bell-CHSH non
locality test, in fact, is significantly reduced when amplification is embedded
into the test itself. Such a beneficial effect holds also in the presence of
detection-inefficiency. Our study helps in affirming noiseless amplification as
a valuable tool for coherent information processing and the generation of
strongly non classical states of bosonic systems.
