Tunneling in rf-SQUIDs and tests of quantum mechanics at the macroscopic level

Superconducting devices such as rf-SQUIDs have been proposed to test the validity of quantum mechanics by means of Bell-like inequalities involving different-time correlation probabilities for measurements of magnetic flux. We calculate the quantum mechanical violations to such temporal Bell inequalities taking into account the effect of the measurement process on the probability distribution for the outcomes. We define a general criterion quantifying the observability of the violations and show that it is not fulfilled for the various experimental configurations proposed so far.