Symmetric Blind Information Reconciliation for Quantum Key Distribution

Quantum key distribution (QKD) is a quantum-proof key-exchange scheme which is fast approaching the communication industry. An essential component in QKD is the information reconciliation step, which is used for correcting the quantum-channel noise errors. The recently suggested blind-reconciliation technique, based on low-density parity-check codes, offers remarkable prospectives for efficient information reconciliation without an a priori quantum bit error rate estimation. We suggest an improvement of the blind-information-reconciliation protocol promoting a significant increase in the efficiency of the procedure and reducing its interactivity. The proposed technique is based on introducing symmetry in operations of parties, and the consideration of results of unsuccessful belief-propagation decodings.

Figure 1

Comparison of three parameters (efficiency, typical number of communication rounds, and convergence guarantee) for different approaches to information reconciliation for QKD systems: the Cascade method [11], straightforward implementation of LDPC codes [16], rate-adaptive implementation of LDPC codes [18], blind reconciliation implementation of LDPC codes [20], and our proposed solution (symmetric blind information reconciliation). We note that the typical number of communication rounds for blind and symmetric blind protocols is considered under the assumption that both of the protocols run until a convergence of the syndrome decoding.

Figure 2

Comparison of the standard blind and symmetric blind-information-reconciliation protocols for two modes of disclosed bit number calculation (6): $\alpha =1$ (left column) and $\alpha =0.5$ (right column). The thin lines and empty symbols stand for blind information reconciliation, while the bold lines and filled symbols represent the suggested approach (symmetric blind information reconciliation). In (a) and (b), the efficiencies, i.e., the ratios of disclosed information to the theoretical limit, are shown as functions of the QBER for the four standard LDPC codes [32] with block length $n=1944$. In (c) and (d), the mean numbers of communication rounds are shown as a function of the QBER. Changes of the codes (corresponding to different $R$’s) are performed according to the requirement that the probability of convergence for the blind reconciliation using only the punctured bits is larger than 90%. The convergence probability for the symmetric blind reconciliation is always 100%.

Figure 3

(a) The efficiency of rate-adaptive symmetric blind reconciliation for two sets of codes and two modes of disclosed bit number is shown as a function of QBER. (b) Mean numbers of additional communication round of rate-adaptive symmetric blind reconciliation for two sets of codes and two modes of disclosed bit number is shown as a function of QBER. The first set of codes is the standard one with block length $n=1944$ [32], and the second set of codes consists of nine codes with rates (7) and block length $n=4000$. The disclosed bit number is chosen according to (6) with $\alpha =1$ (moderate) and $\alpha =0.5$ (diminished).

Figure 4

(a) The block scheme of a symmetric blind-reconciliation-procedure workflow is presented. Note that all summations are assumed to be performed by modulo 2. (b) Visual representation of choosing numbers for shortened and punctured symbols in an extending key according to an estimated level of QBER for a particular code is shown. (c) The correspondence between parity-check matrix and the bipartite Tanner graph is presented. (d),(e) The principles of construction of messages from check node to symbol node and symbol node to check node are shown.