We study a reference frame independent (RFI) quantum key distribution (QKD) protocol using six states for Alice and only four states for Bob, while previous RFI protocols require a six state analyzer for Bob. Our protocol can generate a secure key for any possible phase of the entangled state provided the variation is small compared to the measurement rate, as shown by our numerical key rate analysis. We perform a proof-of-principle experiment using polarization entangled photon pairs. In the presence of a varying rotational phase, we obtain a consistently low error rate of less than 4%, indicating the feasibility of this protocol for QKD. Our RFI protocol is hence beneficial but not limited to applications in a satellite or mobile free-space QKD, where a communication node must limit the resources and restrict the number of measured states to four instead of six.
In (b), a half-wave plate (HWP) rotated about its vertical axis with its fast axis aligned to the horizontally polarized photons is used to induce a phase. It is the first HWP found after the output on the Alice's side; see * in Fig. 1.
The spike in the key rate around 40 s in (b) is attributed to the imperfections in the projective measurements, and variations in the coupling efficiencies caused by changing the phase of the state. Both caused a change in the expectation values that increased C. Furthermore, the spike indicates how a slight change of detection efficiencies could impact the key rate, which future security analyses will need to take in consideration as unreliable measurement devices.
Our selection of the MLM is not restrictive and we could choose other tomography methods.