Enhancing Quantum Key Distribution with Entanglement Distillation and Classical Advantage Distillation

TL;DR

This work addresses secure quantum key distribution (QKD) under realistic, noisy channels by introducing a state-aware two-stage distillation: entanglement distillation (ED) followed by advantage distillation (AD). ED is optimized via an enumeration of bi-local Clifford protocols, while AD employs a fixed repetition-code, enabling finite key rates even in high-noise regimes where ED or AD alone fail. The authors derive security bounds for ED+AD against standard BB84 and six-state protocols and show improvements over AD-only limits, with practical implications for near-term QKD deployments due to modest quantum-resource requirements. The approach applies to depolarizing and pure dephasing noise, offering a flexible framework for tailoring distillation to known noise characteristics and paving the way for robust, high-noise QKD in realistic networks.

Abstract

Realizing secure communication between distant parties is one of quantum technology's main goals. Although quantum key distribution promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find the optimal protocol. We test our scheme for different noisy entangled states and demonstrate its quantitative advantage: our two-stage distillation scheme achieves finite key rates even in the high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key distillation scheme and show that they exceed the previous security bounds with only advantage distillation. Since the advantage distillation part does not introduce further requirements on quantum resources, the proposed scheme is well-suited for near-term quantum key distribution tasks.

Figures (12)

• Figure 1: Illustration of a bi-local Clifford entanglement distillation protocol. Alice and Bob first share some noisy entangled pairs. They then perform local Clifford operations ($C^T$ and $C^\dagger$) on their share of qubits. They measure all pairs except the first pair. If the measurement outcomes of the corresponding entangled pairs coincide, they keep the first unmeasured pair. Otherwise, they discard it.
• Figure 2: Illustration of the ED+AD protocol. The noisy entangled pairs shared by Alice and Bob first undergo entanglement distillation. The successfully distilled pairs are measured. The measurement outcomes (dashed lines) become the input to the advantage distillation protocol. The illustration corresponds to a 4-2-1 protocol, e.g., a concatenation of a 4-1 entanglement distillation protocol with a 2-1 advantage distillation protocol.
• Figure 3: Equivalence of ED+AD and a larger entanglement distillation protocol. The left procedure is the QKD protocol based on two-stage distillation. $P$ is a local Pauli operator chosen from $\{I,X,Y,Z \}$. The red bits are compared via an authenticated channel. If the red bits have the same values, the blue bits are kept as raw secret bits. Since the CNOTs in computational basis commute with the measurement, we use the equivalent quantum picture on the right side to calculate the key rates with the distilled output $\rho_\text{distilled}$. The protocol shown here is a $4$-$2$-$1$ protocol defined in the paper.
• Figure 4: Achievable fidelity - depolarizing noise. For each input fidelity, we enumerate all possible distillation protocols and plot the optimal fidelity achieved by the distillation protocol. The $m$-$1$ protocols are the ED-only protocols. The $m$-$n$-$1$ protocols are ED+AD protocols.
• Figure 5: Achievable BB84 asymptotic key rates - depolarizing noise. For each input fidelity, we enumerate all possible distillation protocols and plot the optimal key rate achieved by the distillation protocol.