  We present a single-photon based device-independent quantum key distribution
scheme secure even against no-signaling eavesdropping, which covers quantum
attacks, as well as ones beyond laws of physics but still obeying the rules for
spatially separated events. The operational scheme is inspired by the
Tan-Walls-Collett (1991) interferometric setup, which used the entangled state
of two exit modes of a 50-50 beamsplitter resulting from a single photon
entering one of its input ports, and weak homodyne measurements at two
spatially separated measurement stations. The physics and non-classically of
such an arrangement has been understood only recently. Our protocol links basic
features of the first two emblematic protocols, BB84 and Ekert91, namely the
random bits of the cryptographic key are obtained by measurements on single
photon, while the security is positively tested if one observes a violation of
a specific Bell inequality. The security analysis presented here is based on a
decomposition of the correlations into extremal points of a no-signaling
polytope which allows for identification of the optimal strategy for any
eavesdropping constrained only by the no-signalling principle. For this
strategy, the key rate is calculated, which is then connected with the
violation of a specific Clauser-Horne inequality. We also adapt this analysis
to propose a self-testing quantum random number generator.
