Fast and Simple Qubit-Based Synchronization for Quantum Key Distribution

We propose Qubit4Sync, a synchronization method for quantum-key-distribution (QKD) setups, based on the same qubits exchanged during the protocol and without requiring additional hardware other than that necessary to prepare and measure the quantum states, in a similar fashion to the clock recovery used in classical communications. Our approach introduces a cross-correlation algorithm with low computational complexity for high channel losses. We test the robustness of our scheme in a real QKD implementation, and we believe it may find application in other quantum communication protocols.

Figure 1

An example of autocorrelation $x_m^{AA}$ for a synchronization string with $L={10}^6$, $N_1=10$, and $c_0=\frac{1}{3}$.

Figure 2

(a) Alice’s string, $s^A$, and Bob’s string, $s^B$, are divided into $N_1$ blocks of length $L_1$ and reshaped into an $L_1\times N_1$ matrix. (b) For each row of the matrix, the FFT is calculated, thus obtaining the matrices $S^A$ and $S^B$. Note that $S^A$ can be calculated in advance. (c) The cross-correlation $X_{u,0}$ of the first columns of $S^A$ and $S^B$ is calculated. The position $u_{\mathrm{opt}}$ that maximizes ${\hat{X}}_{u,0}$ corresponds to the position of the first peak of the cross-correlation $X$. (d) Consider the block of $S^A$ shifted by $u_{\mathrm{opt}}$ rows and calculate the cross-correlation between the remaining columns of $S^A$ and $S^B$. The resulting vector $X_{u_{\mathrm{opt}},j}^{AB}$ is antitransformed so as to obtain $x_{u_{\mathrm{opt}}+j{L}_1}^{AB}$. The $j_{\mathrm{opt}}$ that maximizes $x_{u_{\mathrm{opt}}+j{L}_1}^{AB}$ provides the position of the major peak among the smaller peaks.

Figure 3

The experimental setup.

Figure 4

The ${\mathcal{E}}^I$ between Alice’s and Bob’s clocks, after an interval of 1 s, without Bob changing his clock pace [i.e., using ${\tau }^B=20\mathrm{ns}$ in Eq. (1)]. The mean value of the ${\mathcal{E}}^I$ is $\overline{{\mathcal{E}}^I}\simeq -0.503\mathrm{ms}$.

Figure 5

The robustness of the time-offset analysis for different values of the QBER and a sifted synchronization bit fraction. The plot shows the probability of correctly detecting the time offset, which is estimated through simulation of the algorithm. The red dots correspond to successful synchronization with data generated by our setup. The synchronization string used for this figure has length $L={10}^6$.