Arithmetic Reconciliation for CVQKD: Challenges and Feasibility

TL;DR

This paper addresses reconciliation in CVQKD at low SNR by proposing Arithmetic Reconciliation (AR), which uses Distributional Transform Expansion to map Gaussian measurements to the unit interval and generate $m$ binary subchannels. These subchannels are modeled as binary symmetric channels and reconciled via a Slepian-Wolf framework using LDPC syndrome coding for reverse reconciliation, enabling high quantization efficiency. The authors derive analytical relationships and perform simulations showing reconciliation efficiency can exceed $0.95$ at low $SNR$, with finite-length LDPC codes achieving practical secrecy key matching within a few dB of the Shannon limit. Overall, AR offers a low-complexity, feasible path for CVQKD reconciliation, motivating further exploration with longer codes, broader SNR ranges, and security proofs.

Abstract

Continuous variable quantum key distribution allows two legitimate parties to share a common secret key and encompasses reconciliation protocols. A relatively new reconciliation protocol, Arithmetic Reconciliation, presents low complexity and has increasing reconciliation efficiency with lower SNRs. In this paper, we obtain reconciliation efficiencies for this protocol in realistic scenarios, by means of estimation of mutual information, and we also present rates for sequence match of secret keys by Alice and Bob. Results show that this technique is feasible and promising to continuous variable quantum key distribution applications.

Figures (10)

• Figure 1: Sketch of the complete AR scheme.
• Figure 2: Analytical mutual information between $X$ and $Y$, and estimates of $I(U;V)$, for different SNRs.
• Figure 3: Unit interval and bits assignment, $m=3$.
• Figure 4: BSC illustration in an AR scheme.
• Figure 5: Reconciliation efficiency between $X$ and $V_i$ (solid lines) compared to reconciliation efficiency between $U$ and $V_i$ (dashed lines), considering $m$ subchannels.