Protocol for Detecting the Non-locality of the Multi-Majorana Systems

Majorana zero modes (MZMs) are non-abelian anyons that can be used to build topologically protected qubits. MZMs can encode quantum information non-locally and therefore is potentially useful for building fault tolerant quantum computer. If a multi-Majorana system is physically divided into two subsystems in some special ways, there is always non-trivial quantum correlation between the two parts. However, in physical systems, if the preparation of MZMs fails, the system can include trivial fermionic modes, in which the non-locality no longer present. In our work, we developed a protocol using an entanglement witness to measure the nonlocality of the Majorana systems, and also to distinguish perfect Majorana system from the systems contaminated by fermionic modes. The witness only requires parity measurements, and we also design a platform for potentially performing the protocol experimentally. We found that for a simple example, the probability of success is about 42%. We also looked into the performance of the witness in systems with environmental noise.