Temporal bell inequalities and the uncertainty principle

Various schemes have been proposed to test temporal Bell inequalities either by using macroscopic degrees of freedom as the magnetic flux of a rf-SQUID or microscopic degrees as the occupation number of a two level system. We analyze such proposals and the quantum predictions for the violations of temporal Bell inequalities taking into account the consequences of the Heisenberg principle. These inequalities involve correlation probabilities between subsequent measurements of a dichotomic observable. A criterion for the distinguishability of two states, required to define such correlations, is introduced and linked to the effect of the measurement process and the consequent modification of the state.