The Road to Near-Capacity CV-QKD Reconciliation: An FEC-Agnostic Design

Abstract

New near-capacity continuous-variable quantum key distribution (CV-QKD) reconciliation schemes are proposed, where both the authenticated classical channel (ClC) and the quantum channel (QuC) for QKD are protected by separate forward error correction (FEC) coding schemes. More explicitly, all of the syndrome-based QKD reconciliation schemes found in literature rely on syndrome-based codes, such as low-density parity-check (LDPC) codes. Hence at the current state-of-the-art the channel codes that cannot use syndrome decoding such as the family of convolutional codes (CCs) and polar codes cannot be directly applied. Moreover, the ClC used for syndrome transmission in these schemes is generally assumed to be idealistically error-free, where the realistic additive white Gaussian noise (AWGN) and Rayleigh fading of the ClC have not been taken into account. To circumvent this limitation, a new codeword-based - rather than syndrome-based - QKD reconciliation scheme is proposed, where Alice sends an FECprotected codeword to Bob through a ClC, while Bob sends a separate FEC protected codeword to Alice through a QuC. Upon decoding the codeword received from the other side, the final key is obtained by applying a simple modulo-2 operation to the local codeword and the decoded remote codeword. As a result, first of all, the proposed codeword-based QKD reconciliation system ensures protection of both the QuC and of the ClC. Secondly, the proposed system has a similar complexity at both sides, where both Alice and Bob have an FEC encoder and an FEC decoder. Thirdly, the proposed system makes QKD reconciliation compatible with a wide range of FEC schemes, including polar codes, CCs and irregular convolutional codes (IRCCs), where a near-capacity performance can be achieved for both the QuC and for the ClC. Our simulation results demonstrate that thanks to the proposed regime, the performance improvements of the QuC and of the ClC benefit each other, hence leading to an improved secret key rate (SKR) that inches closer to both the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound and to the maximum achievable rate bound.

Keywords

• Continuous variable quantum key distribution (CV-QKD)
• multidimensional reconciliation
• low-density parity check (LDPC) codes
• irregular convolutional codes (IRCC)
• secret key rate (SKR)
• near-capacity codes