Decoy-state quantum key distribution with two-way classical postprocessing

Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD) protocols when a coherent-state source is used. Previously, data postprocessing schemes based on one-way classical communications were considered for use with decoy states. In this paper, we develop two data postprocessing schemes for the decoy-state method using two-way classical communications. Our numerical simulation (using parameters from a specific QKD experiment as an example) results show that our scheme is able to extend the maximal secure distance from $142\mathrm{km}$ (using only one-way classical communications with decoy states) to $181\mathrm{km}$. The second scheme is able to achieve a 10% greater key generation rate in the whole regime of distances. We conclude that decoy-state QKD with two-way classical postprocessing is of practical interest.

Figure 1

Alice and Bob choose two half EPR pairs and input the quantum circuit as shown above. They discard both control and target qubits if they disagree on the outcomes of measurement on the target qubits. On the other hand, they keep the control qubits as surviving qubits if their measurement outcomes agree.

Figure 2

Plot of the secure regions in terms of error rates for 1-LOCC and Gottesman-Lo EDPs. The regions under the solid lines are proven to be secure due to 1-LOCC EDP, and Gottesman-Lo EDP schemes (for the region under the solid line and dashed line), respectively. For the 1-LOCC EDP, we use Eq. (4). For the Gottesman-Lo EDP, we use Eqs. (6, 8). In the Gottesman-Lo EDP, we optimize the B-P sequence up to 12 steps.

Figure 3

(Color online) Plot of the key generation rate as a function of the transmission distance with the data postprocessing scheme of $\mathrm{GLLP}+\text{decoy}+\mathrm{B}$ steps method. The parameters used are from the GYS experiment [19] listed in Table . The $\mathrm{GLLP}+\text{decoy}+\mathrm{B}$ steps scheme surpasses the scheme with 1-LOCC at a distance of $132\mathrm{km}$. The maximal secure distance using four B steps is $181\mathrm{km}$, which is not far from the upper bound of $208\mathrm{km}$.

Figure 4

(Color online) Plot of the key generation rate as a function of the transmission distance, $\mathrm{GLLP}+\text{decoy}+\text{recurrence}$ method vs $\mathrm{GLLP}+\text{decoy}+1\text{−}\mathrm{LOCC}$ method. Recurrence does have some improvement over 1-LOCC in the whole regime of distances. In particular, the recurrence method increases the key generation rate by more than 10% in our simulation. The maximal secure distance for each case is $142.8\mathrm{km}$ (1-LOCC), $149.1\mathrm{km}$ (recurrence), and $163.8\mathrm{km}$ (one B step), respectively. Here we consider the asymptotic decoy-state QKD case with infinitely long signals. The parameters used are from the GYS experiment [19] listed in Table .

Figure 5

(Color online) Plot of the simulation results for three data postprocessing schemes of the decoy-state protocol, $\text{decoy}+1\text{−}\mathrm{LOCC}$, $\text{decoy}+\text{one}$ B step, and $\text{decoy}+\text{recurrence}$, considering statistical fluctuations. The maximal secure distances of three schemes are 120, 125, and $147\mathrm{km}$, respectively. The parameters used are from the GYS experiment [19] listed in Table .