Device-independent quantum key distribution with generalized two-mode Schr\"odinger cat states

TL;DR

This paper introduces a device-independent quantum key distribution protocol utilizing generalized two-mode Schrödinger cat states, demonstrating its security, optimal parameters, and potential advantages over polarization-based protocols in noisy channels.

Contribution

It develops a new DI-QKD protocol with Schrödinger cat states, providing analytical formulas for key parameters and proposing practical implementation methods.

Findings

Quantum bit error rate is zero over any distance in the channel.

States can always violate a Bell inequality in the protocol.

Protocol outperforms polarization entangled state-based DI-QKD in some regimes.

Abstract

We show how weak non-linearities can be used in a device-independent quantum key distribution (QKD) protocol using generalized two-mode Schr\"odinger 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.