  Zero energy Majorana fermion states (Majoranas) can arise at the ends of a
semiconducting wire in proximity with a superconductor. A first generation of
experiments has detected a zero bias conductance peak in these systems that
strongly suggests these Majoranas do exist; however, a definitive demonstration
of the long-ranged entanglement that is crucial for potential applications in
quantum computing has yet to be carried out. This work discusses two possible
measurement schemes to detect this long-ranged entanglement in a wire system
with two coupled pairs of Majoranas, by varying the coupling between one pair
while measuring the fermion parity of the second pair. First, in a system with
two coupled pairs of Majoranas, we discuss how varying the coupling of one pair
in time, while measuring temporal fermion parity correlations of the second
pair, allows for an experimental probe of long-ranged Majorana entanglement.
Second, we show that the power spectrum of the charge noise (fermion parity
noise) of one pair contains signatures of these correlations, as well as
allowing one to infer the parity relaxation rate.
