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

TL;DR

This paper proposes measurement schemes to detect long-range entanglement and relaxation rates of Majorana fermions in 1D topological superconducting wires, advancing the understanding of their quantum properties.

Contribution

It introduces two novel measurement methods for detecting Majorana entanglement and parity relaxation rates in coupled wire systems.

Findings

Temporal fermion parity correlations reveal long-range Majorana entanglement.

Charge noise power spectrum contains signatures of parity correlations.

Parity relaxation rates can be inferred from noise measurements.

Abstract

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.