Practical high-dimensional quantum key distribution with decoy states

High-dimensional quantum key distribution (HD-QKD) allows two parties to generate multiple secure bits of information per detected photon. In this work, we show that decoy-state protocols can be practically implemented for HD-QKD using only one or two decoy states. HD-QKD with two decoy states, under realistic experimental constraints, can generate multiple secure bits per coincidence at distances over 200 km and at rates similar to those achieved by a protocol with infinite decoy states. Furthermore, HD-QKD with only one decoy state is practical at short distances, where it is almost as secure as a protocol with two decoy states. HD-QKD with only one or two decoy states can therefore be implemented to optimize the rate of secure quantum communications.

Figure 1

Schematic diagram of the DO-QKD setup. Alice and Bob randomly choose to measure in either the arrival-time basis or the frequency basis. In case 1, Alice measures in the frequency basis by applying a normal dispersion (ND). Bob's measurement is only anticorrelated to Alice's if he also measures in the frequency basis by applying an anomalous dispersion (AD). In case 2, Alice measures in the arrival-time basis, and Bob's measurement is only correlated to Alice's if he also measures in the arrival-time basis.

Figure 2

Lower bounds on the secure-key capacity (in bits per coincidence) of decoy-state HD-QKD as a function of transmission distance. Top panels show the case $d=8$ and bottom panels show the case $d=32$. Solid lines with crosses (black) correspond to HD-QKD with infinite decoy states; solid lines (red) correspond to HD-QKD with two weak decoy states of ${\nu }_1=\mu /2$ and an optimized ${\nu }_2$; dashed lines (blue) correspond to HD-QKD with only one decoy state of $\nu =\mu /2$; and dotted lines (green) show the performance of HD-QKD without decoy states. For $\mu =0.01$ and $0.10(d=8$ and $32)$, lines for the infinite-decoy-state and the two-decoy-state protocols are indistinguishable at the plots' scales.

Figure 3

Optimal values of ${\nu }_2$ at different transmission distances for two-decoy-state protocols with $\mu =\{0.01,0.10,0.25\}$ and ${\nu }_1=\mu /2$.