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arXiv:2601.02565

Further Improving the Decoy State Quantum Key Distribution Protocol with Advantage Distillation

Walter O. Krawec

quant-phSubmitted Jan 5, 2026• Announced Jan 7, 2026• 0 citations• Revised Jan 7, 2026 (v2)
v1 · Jan 5, 2026v2 · Jan 7, 2026
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Abstract

In this paper, we revisit the application of classical advantage distillation (CAD) to the decoy-state BB84 protocol. Prior work has shown that CAD can greatly improve maximal distances and noise tolerances of the practical decoy state protocol. However, past work in deriving key-rate bounds for this protocol with CAD have assumed a trivial bound on the quantum entropy, whenever Alice sends a vacuum state in a CAD block (i.e., the entropy of such blocks is taken to be zero). Since such rounds contribute, negatively, to the error correction leakage, this results in a correct, though sub-optimal bound. Here, we derive a new proof of security for CAD applied to the decoy state BB84 protocol, computing a bound on Eve's uncertainty in all possible single and vacuum photon events. We use this to derive a new asymptotic key-rate bound which, we show, outperforms prior work, allowing for increased distances and noise tolerances.

Comments
There is a mistake in my proof on page 12; many thanks to Davide Orsucci for his comments!

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In this paper, we revisit the application of classical advantage distillation (CAD) to the decoy-state BB84 protocol. Prior work has shown that CAD can greatly improve maximal distances and noise tolerances of the practical decoy state protocol. However, past work in deriving key-rate bounds for this protocol with CAD have assumed a trivial bound on the quantum entropy, whenever Alice sends a vacuum state in a CAD block (i.e., the entropy of such blocks is taken to be zero). Since such rounds contribute, negatively, to the error correction leakage, this results in a correct, though sub-optimal bound. Here, we derive a new proof of security for CAD applied to the decoy state BB84 protocol, computing a bound on Eve's uncertainty in all possible single and vacuum photon events. We use this to derive a new asymptotic key-rate bound which, we show, outperforms prior work, allowing for increased distances and noise tolerances.
Quantum Key Distribution (QKD) allows two legitimate parties, Alice and Bob, to share a secret key with information-theoretic security, ensuring that an eavesdropper, Eve, cannot obtain any information about the key. A QKD protocol is provably secure only when the Quantum Bit Error Rate (QBER) is below a certain threshold and, therefore, the presence of noise inherently limits the maximum transmission distance. Advantage Distillation (AD) is a classical post-processing technique that enhances QKD protocols by increasing the maximum acceptable QBER and, thus, allows extending the communication range. AD operates by post-selecting blocks of bits and extracting fewer but highly correlated bits between Alice and Bob, which exhibit a reduced QBER, thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this study, we present a new analytical expression for the secure key rate. This will enable a finite-size secure key length analysis of the decoy state version of the BB84 protocol including AD post-processing.
Quantum conference key agreement (QCKA) protocols utilize GHZ states to establish shared group keys between multiple parties. While previous work has shown that standard Classical Advantage Distillation (CAD) protocols can sometimes benefit QCKA performance, it was unknown if past results were asymptotically tight. In this work, we design a new CAD protocol, "Selective Classical Advantage Distillation (S-CAD)", for QCKA, which generalizes prior QCKA+CAD work and allows the parties to selectively enable or disable CAD. We derive an asymptotic proof of security against general coherent attacks, which outperforms prior work. Finally, we evaluate in a variety of simulated star network topologies, showing when S-CAD can help, and when it is best to disable CAD entirely.
In this work, we prove security of a quantum conference key agreement (QCKA) protocol augmented with a classical advantage distillation (CAD) protocol. We derive a proof of security, in the finite key setting, that is able to bound the secure key rate for any general, coherent, attack. We evaluate the performance of the system, showing our result can improve the noise tolerance of the protocol in some, but not all, scenarios. Specifically, our work can improve key rates in network scenarios where users are not located at equal distances, and where there are asymmetries in the error rate between parties.
Advantage Distillation (AD) is a classical post-processing technique that enhances Quantum Key Distribution (QKD) protocols by increasing the maximum acceptable Quantum Bit Error Rate (QBER) and thus extending the distance at which QKD links can be securely established. AD operates by post-selecting blocks of bits and extracting fewer high-fidelity bits, exhibiting a reduced QBER and thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this work we present the first comprehensive finite key-size analysis of decoy-state BB84 enhanced via AD post-processing. We demonstrate that through the use of AD the maximum acceptable QBER increases from around 9.5%9.5\%9.5% to around 17.3%17.3\%17.3% for realistic key sizes. This result shows that substantial performance enhancements can be achieved in scenarios which are constrained by the maximum tolerable QBER via improvements of the post-processing method alone.
Abstract Quantum key distribution (QKD) provides a promising solution for sharing information-theoretic secret keys between two remote legitimate parties. To improve the maximal transmission distance and the maximal error rate tolerance, we apply the advantage distillation technology to analyze the security of practical decoy-state QKD systems. Based on the practical experimental parameters, the device-dependent QKD protocols and the measurement-device-independent QKD protocols have been respectively analyzed, and our analysis results demonstrate that the advantage distillation technology can significantly improve the performance of various QKD protocols. In the four-state and six-state device-dependent QKD protocols, we prove that the maximal transmission distance can be improved from 142 km to 180 km and from 146 km to 187 km respectively. In the four-state and six-state measurement-device-independent QKD protocols, we prove that the maximal transmission distance can be improved from 195 km to 273 km and from 200 km to 282 km respectively.
The advantage distillation (AD) method can significantly improve the bit error rate tolerance and transmission distance for different quantum key distribution (QKD) protocols. To enhance the transmission distance in a decoy-three-state QKD protocol, we analyze security using the AD method for the decoy-three-state QKD protocol with a weak-coherent source. The theoretical analysis results indicate that the AD method can significantly enhance the transmission distance of the decoy-three-state QKD protocol. Moreover, by applying the AD method, we experimentally realize the decoy-three-state QKD protocol with 130 km transmission distance. Our analysis results demonstrate that the AD method can significantly improve the performance of decoy-three-state QKD protocols, which can be applied in the quantum network in future research.