Device-independent quantum key distribution with generalized two-mode Schrödinger cat states

We show how weak nonlinearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schrödinger cat states. The QKD protocol is therefore shown to be secure against collective attacks and for some coherent attacks. We derive analytical formulas for the optimal values of the Bell parameter, the quantum bit error rate, and the device-independent secret key rate in the noiseless lossy bosonic channel. Additionally, we give the filters and measurements which achieve these optimal values. We find that, over any distance in this channel, the quantum bit error rate is identically zero, in principle, and the states in the protocol are always able to violate a Bell inequality. The protocol is found to be superior in some regimes to a device-independent QKD protocol based on polarization entangled states in a depolarizing channel. Finally, we propose an implementation for the optimal filters and measurements.

Figure 1

The secret key fraction $K$ as a function of the distance between Alice and Bob assuming a loss coefficient of 0.2 dB/km and the optimal $\gamma$ for the specified distance. This plot gives the raw fraction; it does not include finite detection efficiencies, dark counts, thermal noise, or the relative sampling frequency of the $\{A_0,B_1\}$ measurement.

Figure 2

Plot of the critical QBER $Q_{\mathrm{crit}}$ as a function of distance, see text for details. The biphoton approach is superior in the gray region, corresponding to $Q<Q_{\mathrm{crit}}$. The phase-entangled coherent-state approach is superior in the white region, corresponding to $Q>Q_{\mathrm{crit}}$. The discrete-variable DIQKD approach using biphotons cannot be used when the QBER exceeds the dashed black line.