Certified quantum measurement of Majorana fermions

Abstract

We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anti-commutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness W , which satisfies W ≤ 3 for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value W = 5 indicates the degree of confidence in the detection of Majorana fermions.

Scalable noncontextuality inequalities and certification of multiqubit quantum systems

“…We then show that our inequalities can be used for certification of multiqubit quantum systems in the sense of Ref. [32]. In fact, we generalize the results of that work to any number of qubits.…”

“…Here we provide a slightly different definition that takes inspiration from Ref. [32] (see also Ref. [33]) and fits better the inequalities introduced here.…”

“…Since we do not specify the dimension of the underlying Hilbert space, without any loss of generality, we can assume that the measurements are projective and the state is pure (see, e.g., Ref. [32]). In other words, any correlations obtained within the above experiment can always be reproduced with a pure state and projective measurements satisfying the same compatibility relations.…”

“…On the other side, they have also been used for certification of relevant quantum properties such as the dimension of the underlying quantum system [28,29]. More importantly, contextuality and temporal correlations have also been exploited for certification of quantum states and/or measurements [30][31][32][33][34].…”

Sum-of-squares decompositions for a family of noncontextuality inequalities and self-testing of quantum devices

“…However, the observed statistics are unchanged in the presence of auxiliary degrees of freedom (or auxiliary systems) and a global unitary. Therefore, self-testing in the context of state-dependent quantum contextual correlation [BRV + 19b,IMOK20] To obtain self-testing only from the reduced Assumptions mentioned in section 1, we consider a modified version of the expression B n (40) of the following form…”