Continuous-variable Measurement-device-independent Quantum Relay Network with Phase-sensitive Amplifiers

Continuous-variable (CV) measurement-device-independent (MDI) quantum cryptography is now heading towards solving the practical problem of implementing scalable quantum networks. In this paper, we show that a solution can come from deploying an optical amplifier in the CV-MDI system, aiming to establish a high-rate quantum network. We suggest an improved CV-MDI protocol using the EPR states coupled with optical amplifiers. It can implement a practical quantum network scheme, where the legal participants create the secret correlations by using EPR states connecting to an untrusted relay via insecure links and applying the multi-entangled Greenberger-Horne-Zeilinger (GHZ) state analysis at relay station. Despite the possibility that the relay could be completely tampered with and imperfect links are subject to the powerful attacks, the legal participants are still able to extract a secret key from network communication. The numerical simulation indicates that the quantum network communication can be achieved in an asymmetric scenario, fulfilling the demands of a practical quantum network. Furthermore, we show that the use of optical amplifiers can compensate the inherent imperfections and improve the secret key rate of the CV-MDI system.