Self-testing Majorana parity measurements

Presenting Author: Karl Mayer, University of Colorado
Contributing Author(s): Abu Irfan, Gerardo Ortiz, Emanuel Knill

We present a self-testing protocol for certifying a set of Majorana parity operators under minimal physical assumptions. The scenario involves measurements which ideally are of parities acting on two logical qubits encoded in six Majorana modes. Our only assumptions are that an unknown state is repeatedly prepared, that the measurements are two-outcome POVMs, and that measurements corresponding to disjoint modes are compatible. We prove a rigidity theorem stating that an observation of the ideal statistics implies that the prepared state is contained in a subspace on which the action of the measurement operators is equivalent to that of ideal parities. The proof is based on a mapping between Majorana parities and two qubit Pauli operators arranged in a Peres-Mermin magic square. A version of the protocol robust to errors is the subject of ongoing work. A successful application of such a protocol would constitute strong evidence for the existence of Majorana zero modes, which are potential building blocks for a topological quantum computer.

(Session 5 : Sunday from 5:00pm - 7:00pm)


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