Measurement-device-independent quantum key distribution (MDI-QKD) has attracted widespread attention due to its effective defense against attacks on the detection side. However, its key generation rate is limited by the success probability of two-photon interference, which drops sharply under high channel loss and thereby limits high-throughput long-distance communication. moreover, each successful interference event yields only 1 bit of key information. To overcome these limitations, we propose the introduction of the multi-scale entanglement renormalization ansatz (MERA) into the MDI-QKD protocol. This constructs a hierarchical entanglement structure capable of efficiently encoding multi-bit information, aiming to significantly enhance the key rate, extend communication distance, and maintain theoretical security.
We design three MERA-based MDI-QKD implementation schemes:
(1) A single-photon scheme based on the compressed single-photon state at the L-th layer of MERA, which compresses multi-layer information into a single-photon state, enabling the extraction of multiple key bits from a single successful interference event, making it suitable for short-to-medium distance scenarios requiring high key rates;
(2) An entanglement-based scheme based on the compressed entangled state at the (L-1)-th layer of MERA, which leverages the strong correlations of entangled states to enhance noise resistance, making it suitable for long-distance and high-loss channels;
(3) A hybrid adaptive scheme that dynamically switches between the above two modes based on real-time channel quality, achieving optimal performance adaptation across all distances.
All schemes employ the hierarchical compression mechanism of MERA, utilizing the disentangling operator U and the isometric mapping operator W to compress the quantum state layer by layer, and reconstructing the state via inverse operations for multi-level key extraction. The protocol incorporates the decoy-state method for eavesdropping detection, and uses basis sifting and multi-layer fidelity verification to ensure information integrity and security. Additionally, by designing four predefined MERA topological structures, efficient structural matching and information synchronization are achieved.
Numerical simulations show that,Within the 0–200 km range, the single-photon scheme SI-MERA-MDI-QKD improves the key generation rate by approximately 22931% compared to classical MDI-QKD. The entanglement-based scheme ES-MERA-MDI-QKD and the hybrid scheme HY-MERA-MDI-QKD still maintain an effective key rate of 10^-11 bit/pulse at 350 km, extending the effective communication distance of classical MDI-QKD by approximately 150 km.
Under varying detector efficiencies and channel loss conditions, the proposed schemes all demonstrate significant performance advantages. Coding capacity analysis shows that, under zero-error conditions, the encoding capability of MERA-MDI-QKD can exceed that of classical MDI-QKD by more than 221 times.
Security analysis shows that the proposed schemes exhibit strong robustness against collective attacks, intercept-resend attacks, and Trojan-horse attacks. Under collective attacks, any eavesdropping behavior leads to the non-orthogonality of ancillary states, resulting in detectable errors. Under intercept-resend attacks, attackers struggle to reconstruct the original entanglement structure. Under Trojan-horse attacks, the protocol still maintains a high secure key rate through multi-layer encoding.