Quantum Key Distribution Based on Systematic Polar Coding

TL;DR

This work introduces Polar-code QKD, a protocol that integrates systematic polar coding into the quantum phase of QKD to boost key rates in finite-size, low-error channels. By encoding the frozen bits with a prior-round key and performing parameter estimation via frozen-bit comparisons, the scheme reduces key-rate penalties from classical reconciliation. The authors derive finite-size key-rate expressions and demonstrate, through comparative analysis, that Polar-code QKD achieves higher rates than BB84-QKD and eBB84-QKD for practical block sizes (e.g., N = 2^{16} and N = 2^{17}) and modest error thresholds E. The approach highlights the practical potential of combining quantum communication with structured classical coding to enhance secure key distribution in realistic settings.

Abstract

Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction algorithm) frameworks - quantum key distribution based on systematic polar coding. This results in obtaining key rates greater than standard quantum key distribution (BB84) and its efficient version (eBB84) when finite-size regime and lower-error-rate quantum channel are considered.

Figures (3)

• Figure 1: Block diagram of a round-wise QKD scheme.
• Figure 2: Key rate comparison between BB84-QKD ($r^{\text{BB84}}(e)$, dashed (red) line), Polar-code QKD ($r(e,E)$, solid (black) line), and eBB84-QKD ($r^{\text{eBB84}}(e)$, dotted (blue) line) in the case of $N=2^{16}$. The Polar-code QKD rate $r(e,E)$ is given for several values of quantity $E$: solid line—$E$$=$$0.04$; solid $*$ line—$E$$=$$0.03$; solid $\cross$ line—$E$$=$$0.02$; solid $\mathbin{\blacklozenge}$ line—$E$$=$$0.03$. Note that the BB84-QKD rate $r^{\text{BB84}}(e)$ does not depend on $E$. The infinite-slope ending of $r(e,E)$ is due to polar coding performance— the polar coding corrects errors up to error rates of $E$; i.e., Polar-code QKD does not operate for error rates above $E$.
• Figure 3: Key rate comparison between BB84-QKD ($r^{\text{BB84}}(e)$, dashed (red) line), Polar-code QKD ($r(e,E)$, solid (black) line), and eBB84-QKD ($r^{\text{eBB84}}(e)$, dotted (blue) line) in the case of $N=2^{17}$. The Polar-code QKD rate $r(e,E)$ is given for several values of quantity $E$: solid line—$E$$=$$0.04$; solid $*$ line—$E$$=$$0.03$; solid $\cross$ line—$E$$=$$0.02$; solid $\mathbin{\blacklozenge}$ line—$E$$=$$0.03$. Note that the BB84-QKD rate $r^{\text{BB84}}(e)$ does not depend on $E$. The infinite-slope ending of $r(e,E)$ is due to polar coding performance— the polar coding corrects errors up to error rates of $E$; i.e., Polar-code QKD does not operate for error rates above $E$.

Theorems & Definitions (1)

• Example 1