Experimental comparison of various quantum key distribution protocols under reference frame rotation and fluctuation
Introduction
Quantum key distribution (QKD), one of the most mature quantum information technologies, provides a way to distribute secrete keys between distant parties of Alice and Bob with the security being guaranteed by the laws of quantum physics [1], [2]. There has been enormous effort to improve the security and practicality of the QKD both in theory and experiment [3], [4], [5], [6], [7], [8]. Recently, satellite based free-space QKD has attracted a lot of attention since it overcomes the communication distance limit of optical fiber based QKD [9], [10], [11], [12], [13]. Indeed, it has been recently reported that intercontinental QKD communication is possible via satellite quantum communication [14]. Note that, in free-space QKD, polarization is the most commonly chosen degree of freedom for qubit encoding due to the robustness and simplicity for implementation.
In order to implement QKD, it is usually required to share a common reference frame between Alice and Bob. In free-space QKD, the polarization axes should be aligned and maintained during the communication. However, in satellite QKD, it can be difficult and costly to maintain the polarization axes alignment due to the revolution and rotation of the satellite with respect to the ground station [15]. Reference-frame-independent (RFI) QKD provides an efficient way to solve this problem [16], [17], [18], [19]. Note that the hardware requirement for RFI-QKD is comparable to those of BB84 or six-state protocols. In the RFI-QKD protocol, the secret keys are shared via the basis which is not affected by the reference frame rotation and fluctuation while the security is checked by other two non-commuting bases. Note that the RFI-QKD can be applied to measurement-device-independent QKD which provides stronger communication security [20], [21].
In the original proposal and following experimental implementation, the security of RFI-QKD has been discussed only when the reference frames of Alice and Bob are rotated with a fixed angle, so there is no relative change between the reference frames during the communication [16], [17], [18], [19]. In practice, however, the reference frame of satellite with respect to the ground station continuously changes. There has been only a few theoretical studies to analyze the security of RFI-QKD under the continuously changing reference frames [22], [23], however, there has been no experimental verification.
In this paper, we have both theoretically and experimentally investigated various QKD protocols including BB84, six-state, and RFI-QKD protocols under the reference frame rotation and fluctuation. By comparing the secret key rates of various QKD protocols, we have verified that RFI-QKD indeed outperforms other QKD protocols under the continuously changing reference frames.
Section snippets
Theory
Let us suppose that Alice prepares a single-photon state in the polarization state either along or or bases and sends it to Bob. Here, , , and bases form mutually unbiased bases in a single qubit or a two dimensional Hilbert space. It is typical to define , , and bases as , , and bases, where H, V, D, A, R, and L denote horizontal, vertical, diagonal (45), anti-diagonal (-45), right circular, and left circular polarization states, respectively. Assuming the
Experimental setup
The experimental setup to investigate various QKD protocols under the reference frame rotation and fluctuation is depicted in Fig. 3. Alice prepares coherent pulses with the polarization state of either or using six identical lasers and linear optical elements. The wavelength and pulse width of the coherent pulses are 780 nm and 3 ns, respectively. The repetition rate of the system is 100 MHz. The coherent pulses from different lasers pass through a single-mode fiber
Conclusion
In summary, we have experimentally demonstrated various QKD protocols of BB84, six-state, and RFI-QKD protocols under the reference frame rotation and fluctuation. In both cases, the QBER of RFI-QKD protocol is invariant while that of other QKD protocols increases as the amount of reference frame rotation and fluctuation increases. With QBER and parameter of RFI-QKD, we have verified that RFI-QKD protocol provides the highest secrete key rate among the employed QKD protocols under the
Acknowledgments
This work was supported by the ICT R&D program of MSIP/IITP, Republic of Korea (B0101-16-1355), and the KIST, Republic of Korea research program (2E29508).
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