Measurement-Device-Independent Twin-Field Quantum Key Distribution

Abstract

The ultimate aim of quantum key distribution (QKD) is improving the transmission distance and key generation speed. Unfortunately, it is believed to be limited by the secret-key capacity of quantum channel without quantum repeater. Recently, a novel twin-field QKD (TF-QKD) is proposed to break through the limit, where the key rate is proportional to the square-root of channel transmittance. Here, by using the vacuum and one-photon state as a qubit, we show that the TF-QKD can be regarded as a measurement-device-independent QKD (MDI-QKD) with single-photon Bell state measurement. Therefore, the MDI property of TF-QKD can be understood clearly. Importantly, the universal security proof theories can be directly used for TF-QKD, such as BB84 encoding, six-state encoding and reference-frame-independent scheme. Furthermore, we propose a feasible experimental scheme for the proof-of-principle experimental demonstration.

Figure 1

Scheme to overcome the PLOB bound of QKD. (a) Setup for entanglement-based MDI-QKD with single-photon BSM. Alice and Bob prepare single-photon Bell state, while Charlie implements entanglement swapping. M represents the measurement operation, such as Z, X and Y basis. Alice and Bob implement the M measurement operation after Charlie performs the single-photon BSM. (b) Prepare-and-measure MDI-QKD with single-photon BSM. Alice and Bob directly prepare the qubit with superpositions of the vacuum and one-photon states. Alice and Bob implement the M measurement operation before Charlie performs the single-photon BSM. (c) Effective TF-QKD with single-photon and laser sources. The photons from single-photon source and laser source are indistinguishable in every degree of freedom. The phase-reference of long-distance should be stabilized to implement laser interference. The single-photon source is used to implement Z basis encoding, while the laser source is used to implement the phase encoding, such as X and Y basis.

Figure 2

The practical TF-QKD setup. (a) practical TF-QKD with independent lasers. The phase modulator (PM) can realize phase encoding and random phase modulation at one time. CW-Laser: continuous-wave laser, AM: amplitude modulator, VOA, variable optical attenuator, BPF: band pass filter, PC: polarization controller, BS: beam splitter, RNG: random number generator. (b) Phase self-aligned TF-QKD with single laser. The Faraday mirror (FM) or the polarization beam splitter (PBS) and the π/2 Faraday rotator (FR) are exploited to realize the transformation between horizontal and vertical polarizations. Alice and Bob could choose to prepare the qubit in Z basis by using Charlie’s laser or their own pulse lasers. The security will be enhanced if they use their own laser. Some polarization-maintaining fiber are required to keep the polarization in the systems of Alice, Bob and Charlie. P-Laser: pulse laser, OS: optical switch, PD, photoelectric detector, Cir: circulator.

Figure 3

The key rate of practical TF-QKD with BB84 encoding in the asymptotic limit. For each transmission loss, we optimize the parameters μ and t with e_opt = 1%, ν = 0.1, ω = 0.02 and M = 16. For the PLOB bound, we use $R_{\mathrm{PLOB}}=-{\log }_2\mathrm{(1}-{\eta }_{\mathrm{PLOB}})$, η_PLOB = η_d × 10^−0.02L. The secure key rate of TF-QKD with BB84 encoding can surpass the PLOB bound under the case of detector with η_d = 40%, p_d = 10⁻⁷, the performance of detector has been realized much more.

Figure 4

The key rates of practical TF-QKD with BB84 encoding and RFI scheme in the asymptotic limit. For each transmission loss, we optimize the parameters μ and t with η_d = 90%, p_d = 10⁻⁹, ν = 0.1, ω = 0.02 and M = 16. The secure key rate of practical TF-QKD with RFI scheme do not change obviously with optical error rate e_opt. The secure key rate of practical TF-QKD with BB84 encoding can also beat the PLOB bound even the optical error rate up to e_opt = 20%.