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

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.

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• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Milestones toward Majorana-based quantum computing
• Multi-channel Kondo impurity dynamics in a Majorana device
• A note on the Full Counting Statistics of paired fermions
• A Proposal to Measure the Quasiparticle Poisoning Time of Majorana Bound States
• Spin Transfer of Quantum Information between Majorana Modes and a Resonator
• Universal two-time correlations, out-of-time-ordered correlators and Leggett-Garg inequality violation by edge Majorana fermion qubits
• Correlated parity measurements as a probe of non-abelian statistics in 1D superconducting wires
• Demonstrating Entanglement by Testing Bell's Theorem in Majorana Wires
• Majorana fermions in the nonuniform Ising-Kitaev chain: exact solution
• Parafermion stabilizer codes
• Controlling Majorana hybridization in magnetic chain-superconductor systems
• Nonuniform Parafermion Chains: Low-Energy Physics and Finite-Size Effects