Device-Independent Quantum Cryptography for Continuous Variables

We present the first device-independent quantum cryptography protocol for continuous variables. Our scheme is based on the Gottesman-Kitaev-Preskill encoding scheme whereby a qubit is embedded in the infinite-dimensional space of a quantum harmonic oscillator. The novel application of discrete-variable device-independent quantum key distribution to this encoding enables a continuous-variable analogue. Since the security of this protocol is based on discrete-variables we inherit by default security against collective attacks and, under certain memoryless assumptions, coherent attacks. We find that our protocol is valid over the same distances as its discrete-variable counterpart, except that we are able to take advantage of high efficiency commercially available detectors where, for the most part, only homodyne detection is required. This offers the potential of removing the difficulty in closing the loopholes associated with Bell inequalities.