A hierarchy in Majorana non-abelian tests and hidden variable models

Abstract

The recent progress of the Majorana experiments paves a way for the future tests of non-abelian braiding statistics and topologically-protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary in order to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity.

5 pages, 4 figures, 5 page supplementary

References in corpus (24)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Research on Hidden Variable Theories: a review of recent progresses
• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Ballistic superconductivity in semiconductor nanowires
• No extension of quantum theory can have improved predictive power
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• A Parity-Protected Superconductor-Semiconductor Qubit
• Local hidden--variable models for entangled quantum states
• Quantized conductance of Majorana zero mode in the vortex of the topological superconductor (Li0.84Fe0.16)OHFeSe
• Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$
• Closing of the Induced Gap in a Hybrid Superconductor-Semiconductor Nanowire
• Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions
• Destructive Little-Parks Effect in a Full-Shell Nanowire-based Transmon
• Nonlocal conductance spectroscopy of Andreev bound states in gate-defined InAs/Al nanowires
• Recent progress on Majorana in semiconductor-superconductor heterostructures--Engineering and detection
• Parametric exploration of zero-energy modes in three-terminal InSb-Al nanowire devices