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

Measuring fermion parity correlations and relaxation rates in 1D topological superconducting wires