Robustness of reference-frame-independent quantum key distribution against the relative motion of the reference frames

Reference-Frame-Independent quantum key distribution (RFI-QKD) is known to be robust against slowly varying reference frames. However, other QKD protocols such as BB84 can also provide secrete keys if the speed of the relative motion of the reference frames is slow enough. While there has been a few studies to quantify the speed of the relative motion of the reference frames in RFI-QKD, it is not yet clear if RFI-QKD provides better performance than other QKD protocols under this condition. Here, we analyze and compare the security of RFI-QKD and BB84 protocol in the presence of the relative motion of the reference frames. In order to compare their security in real world implementation, we also consider the QKD protocols with decoy state method. Our analysis shows that RFI-QKD provides more robustness than BB84 protocol against the relative motion of the reference frames.