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

TL;DR

The paper tackles improving decoy-state BB84 QKD by incorporating classical advantage distillation (CAD) with a security proof that accounts for blocks containing vacuum rounds, addressing a gap in previous entropy bounds.A new asymptotic key-rate bound is derived by bounding Eve’s uncertainty for blocks with both vacuum and single-photon events, and this bound is then integrated with decoy-state analysis to bound unobservable quantities.Across both infinite and two-decoy implementations and for four- and six-state BB84, the results show longer secure distances and higher noise tolerance compared to prior CAD analyses, with the new bound never decreasing relative to earlier work.Overall, the work demonstrates that CAD can further enhance practical decoy-state QKD performance and provides a framework that may inspire tighter finite-key analyses and applications to other QKD protocols.

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.

Figures (5)

• Figure 1: Comparing our new result (Solid lines, Equation \ref{['eq:security:main-equation-result']}) with prior work in li2022improving (Dashed lines) for the four-state BB84 protocol using infinite decoy states. We test a CAD block size of $C=2$ (Blue/Red), $C=3$ (Yellow/Purple), and $C=8$ (Green/Orange). We note that in all cases, our result outperforms prior work, allowing for increased distances. Here we set $e_{det} = 0.05$, $p_d=10^{-6}$, and $f = .04$. We also use $\mu = 0.48$. A comparison to the case without CAD is also shown (Black Solid line). Right: Similar to the left graph, but showing smaller distances ranging from $1$ to $50km$. Here we note that there is no difference in our result and prior work; furthermore, we note that CAD actually hinders performance. Thus CAD should only be utilized at suitably high distances.
• Figure 2: Comparing key-rate between our new result (solid) and prior work (dashed) as noise increases for a fixed distance of $d=50km$ (Left) and $d=170km$ (Right). We see that at high distances, our result outperforms prior work, including standard decoy state results without CAD, allowing for increased noise tolerance. At lower distances, our work is numerically equivalent to prior work.
• Figure 3: Comparing our work (solid lines) with prior work (dashed lines) for the six state decoy BB84 protocol. Left: We fix $e_{det} = 0.05$ and vary the distance; Right: We fix the distance at $d=170km$ and vary the noise $e_{det}$. Note that in all cases, our work outperforms prior work. We also note that CAD can substantially improve decoy state performance, as originally observed in li2022improving. Not surprisingly, six-state BB84 outperforms the four state version.
• Figure 4: Comparing our work (solid lines) with prior work (dashed lines) for the two-decoy BB84 protocol. Left: We fix $e_{det} = 0.05$ and vary the distance; Right: We fix the distance at $d=170km$ and vary the noise $e_{det}$. As expected, the two-decoy protocol does not perform as well, asymptotically, as the infinite decoy version, however the difference is not very substantial; we also note that, as before, our work produces better results.
• Figure 5: Comparing our work (solid lines) with prior work (dashed lines) for the two-decoy, six-state, BB84 protocol. Left: We fix $e_{det} = 0.05$ and vary the distance; Right: We fix the distance at $d=170km$ and vary the noise $e_{det}$.

Theorems & Definitions (5)

• Theorem 1
• Lemma 1
• proof
• Theorem 2
• proof