Measurement-Device-Independent Quantum Key Distribution Over a 404 km Optical Fiber

Measurement-device-independent quantum key distribution (MDIQKD) with the decoy-state method negates security threats of both the imperfect single-photon source and detection losses. Lengthening the distance and improving the key rate of quantum key distribution (QKD) are vital issues in practical applications of QKD. Herein, we report the results of MDIQKD over 404 km of ultralow-loss optical fiber and 311 km of a standard optical fiber while employing an optimized four-intensity decoy-state method. This record-breaking implementation of the MDIQKD method not only provides a new distance record for both MDIQKD and all types of QKD systems but also, more significantly, achieves a distance that the traditional Bennett-Brassard 1984 QKD would not be able to achieve with the same detection devices even with ideal single-photon sources. This work represents a significant step toward proving and developing feasible long-distance QKD.

Figure 1

Experimental setup for the MDIQKD system. Alice’s (Bob’s) phase randomized weak coherent state pulses are modulated into four decoy-state intensities via two intensity modulators (IM). An asymmetrical Mach-Zehnder interferometer (AMZI), two IMs, and one phase modulator (PM) encode time-bin phase qubits. A circulator (Circ) is used to isolate the laser with the quantum signal. A phase shifter (PS) is used to compensate the relative phase fluctuation of two AMZIs. The first IM is used to better format the signal pulse; the following two IMs are used to modulate the decoy state, and the final two IMs are used for time-bin qubit encoding. TC, temperature controller; AC, alternating current; DC, direct current; Att., attenuator; DWDM, dense wavelength division multiplexer; BS, beam splitter; SNSPD, superconducting nanowire single-photon (SP) detector.

Figure 2

MDIQKD key rates versus the intensities, ${\mu }_z$, and probabilities, $p_z$. (a) The key rates of a 102 km standard fiber with a 10-minute data accumulation time. By varying the signal state intensities, ${\mu }_z$, and probabilities, $p_z$, we can achieve key rates from 321 to 7.9 bps with a failure probability of ${10}^{-10}$. (b) The key rates of the same experimental data without the finite size effect. The key rates are more than 1.5 kbps for all signal state intensities, ${\mu }_z$, and probabilities, $p_z$.

Figure 3

Experimental results. The experimental results (symbols) agree well with the theoretical simulations (solid lines) with a maximum transmission distance of 404 km via ultralow-loss optical fiber and 311 km via standard optical fiber. For comparison, we include simulations for the balanced basis passive Bennett-Brassard 1984 (BB84) protocol using ideal SP sources, the practical SP with $g^{(2)}(0)=0.01$ without the decoy-state method, the WCS with the decoy-state method, and the results of Ref. [12] shown as the dotted lines. Note that even though the MDIQKD produces lower key rates than the BB84 protocol, it can offer greater secure transmission distances.