Robustness of reference-frame-independent quantum key distribution against the relative motion of the reference frames
Introduction
Quantum key distribution (QKD) promises enhanced communication security based on the laws of quantum physics [1], [2]. Since the first QKD protocol has been introduced in 1984, there has been a lot of theoretical and experimental effort to improve the security and the practicality of QKD [3], [4]. These days, QKD research is not only limited in laboratories [5], [6], [7], [8], [9] but also in industries.1
In general, QKD requires a shared common reference frame between two communicating parties, Alice and Bob. For example, the interferometric stability or the alignment of the polarization axes are required for fiber based QKD using phase encoding and polarization encoding free-space QKD, respectively. However, it can be difficult and costly to maintain the shared reference frame in real world implementation. For instance, it is highly impractical to establish a common polarization axes in earth-to-satellite QKD due to the revolution and rotation of the satellite with respect to the ground station [10], [11], [12], [13], [14], [15], [16].
A recently proposed reference-frame-independent QKD (RFI-QKD) provides an efficient way to bypass this shared reference frame problem [17]. In RFI-QKD, Alice and Bob share the secrete keys via a decoherence-free basis while check the communication security with other bases. Both free-space [18] and telecom fiber [19], [20] based RFI-QKD have been successfully implemented. It is remarkable that the concept of the reference frame independent can be applied to measurement-device-independent QKD [21], [22].
Unlike to its name, however, the security of the original theory of RFI-QKD is guaranteed when the relative motion of the reference frames is slow comparing to the system repetition rate [17]. It is because the eavesdropper information is bounded by the entanglement left in the bipartite state shared between Alice and Bob which is independent of the relative motion of the reference frames. [23]. If the reference frames of Alice and Bob are deviated with a fixed angle, however, one can easily compensate the deviation and implement an ordinary QKD protocol. Therefore, the effectiveness of RFI-QKD over other QKD protocols becomes clear when there is rapid relative motion of the reference frames during the QKD communication. There has been few studies to quantify the speed of the relative motion of the reference frames in RFI-QKD [24], [25]. Without the performance comparison with other QKD protocols, however, these studies do not show the effectiveness of RFI-QKD over other QKD protocols.
In this paper, we report the security of RFI-QKD and BB84 protocol in the presence of the relative motion of the reference frames of Alice and Bob. In order to compare the performances in real world implementation, we also consider the decoy state method. By comparing the security analyses, we found that RFI-QKD is more robust than BB84 protocol against the relative motion of the reference frames.
Section snippets
QKD with a fixed reference frame deviation
In this section, we review the security proof of RFI-QKD and BB84 protocol with a fixed reference frame deviation. A shared reference frame is required for both fiber based QKD with phase and free-space QKD with polarization encoding. It corresponds to the interferometric stability and the polarization axes for fiber based QKD and free-space QKD, respectively. In the following, we will consider free-space QKD with polarization encoding for simplicity. However, we note that our analysis is also
QKD in the presence of the relative motion of reference frames
In this section, we study the effect of the relative motion of the reference frames of Alice and Bob during the QKD communication. Let us consider the case when θ varies from −δ to δ as depicted in Fig. 1. For simplicity, we assume that θ is centered at 0 and equally distributed over .
The quantities , , and C are affected by the relative motion of the reference frames. However, is unchanged since all the time. In order to quantify the effect of the relative motion, we
RFI-QKD and BB84 protocol using decoy state method
In this section, we apply the security analysis to a real world implementation using weak coherent pulses with decoy state method. In the following, we will consider two decoy states method which is most widely used for real world implementation [26]. According to this method, Alice randomly modulates the intensity of the weak coherent pulses with mean photon numbers per pulse of μ, ν and 0 where . They are usually called signal, decoy and vacuum pulses, respectively.
Assuming that the bases
Conclusions
To summary, we have studied both reference frame independent quantum key distribution (RFI-QKD) and BB84 protocol with the presence of the relative motion between the reference frames of Alice and Bob. We have also considered overall noise model with a depolarizing channel between Alice and Bob. In order to compare the secrete key rates in real world implementation, we also have applied the security analyses to the decoy state methods. We found that RFI-QKD provides more robustness than BB84
Acknowledgements
This work was supported by the ICT R&D program of MSIP/IITP (B0101-16-1355), and the KIST research programs (2E27231, 2V05340).
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