Reference-frame-independent measurement-device-independent quantum key distribution using hybrid logical basis

The multiple-qubit logical basis, originally introduced in the context of fault-tolerant quantum computing in decoherence-free subspace (DFS), has specific applications for resolving a reference frame misalignment problem in quantum information protocols. In this paper, an alignment-free MDI-QKD scheme is proposed with rotational-invariant state, which is immune to the collective noise induced by misalignment between two distant legitimate parties. In our protocol, the initial logical qubit is created in the polarization-orbit angular momentum hybrid space, while the transmission is entirely done in the rotation-invariant DFS under the collective noise associated with misalignment. The partial Bell state measurement is performed on the logical qubits to sort the logical Bell state. Compared with the original MDI-QKD protocols, the numerical simulations show that our modified scheme has apparent improvements both in transmission distance and key generation rate. Furthermore, only ordinary optical elements are required in our protocol.