Experimental Asynchronous Measurement-Device-Independent Quantum Cryptographic Conferencing

TL;DR

This work significantly boosts the key rate to $R\sim O(\eta)$, which is independent of the number of users, and thus demonstrating greater application potential, and provides a scalable solution for the development of large-scale quantum communication networks in the future.

Abstract

The quantum cryptographic conferencing (QCC) protocol, which distributes identical secure keys to user groups, is a crucial component of the quantum network. Previous experimental works have implemented the measurement-device-independent (MDI) QCC, of which the key rate in an $N$-user network scales down as $R\sim O(η^N)$, respectively. Building on the MDI QCC protocol, the asynchronous MDI (AMDI) QCC protocol theoretically integrates the mode pairing scheme into QCC, significantly boosting the key rate to $R\sim O(η)$, which is independent of the number of users, and thus demonstrating greater application potential. Experimentally, in this work, we implement the three-user AMDI QCC network without global phase tracking by adopting the fast Fourier transform-based frequency difference estimation and the phase drift compensation technique. Finally, we achieve a key rate of about $4.470\times10^{-9}$ bits per pulse under a maximum overall loss of about 59.6 dB. This work provides a scalable solution for the development of large-scale quantum communication networks in the future.

Figures (8)

• Figure 1: Experimental setup of asynchronous measurement-device-independent quantum cryptographic conferencing (AMDI QCC). (a) Scheme of AMDI QCC network. The user transmits the encoded pulses to the multipath interferometer at the detection node for measurement. (b) The user node. Each user employs an independent free-running laser as the light source. The encoder section consists of cascaded three intensity modulators and two phase modulators, which perform decoy state and 16-slice random phase modulation, respectively. (c) The time sequence diagram of pulses prepared by users. The complete pulse sequence comprises the reference pulses for frequency difference and interferometer phase drift estimation, the quantum pulses for key generation, and the recovery region between reference and quantum pulses. Abbreviation of the components: BS, beam splitter; IM, intensity modulator; PM, phase modulator; DWDM, dense wavelength division multiplexer; VOA, variable optical attenuator; FPC, fiber polarization controller; PMPBS, polarization-maintaining polarization beam splitter; PMBS, polarization-maintaining beam splitter; SNSPD, superconducting nanowire single-photon detector.
• Figure 2: Frequency differences estimation test results and beating frequency measurement results between (a) users AB, and (b) users AC in 5 hours.
• Figure 3: Phase drift compensation and X-basis QBER. (a) Relationship between the X-basis QBER of the reference pulses and the total phase difference of the paired pulses after frequency difference compensation. The visibility of GHZ-HOM interference obtained by fitting the experimental data is about 0.22. The horizontal shift between the dark blue and orange cosine curves measured with a time interval of approximately 1000 seconds in the figure indicates the drift of the additional phase $\Delta \varphi$. (b) Estimated phase drift of the interferometer. We regard the phase slice value corresponding to the minimum QBER point in the figure (b) as the phase shift estimation value. In the calculations, we compute the phase values within the range of 0 to $2\pi$, and thus an abrupt change occurs in the phase shift values when the phase exceeds this range. (c) X-basis QBER of quantum pulses with and without phase compensation. After compensating the frequency difference and phase drift in the test, the X-basis QBER is reduced from about 50.02% to about 40.76%, with a theoretical minimum value of about 37.50% (black dashed line).
• Figure 4: Key generation results of the AMDI QCC in this work, and MDI QCC in PhysRevLett.133.210803du_experimental_2025. The dashed curves in the figure represent theoretical key rates corresponding to scenarios with data accumulation time of about $5\times 10^3$, $2\times 10^4$, and $8\times 10^4$ seconds, respectively. The parameters used in the simulation are given in the Supplemental Material. For comparison, the experimental results of the prior works cited in the figure are calculated based on the data provided in those references.
• Figure S1: Three-user AMDI QCC pulse pairing scheme. The table on the right shows the correspondence between the paired pulses of different users and the single-count events from different interferometer branches in the experiment, in which the $e$ and $l$ represent the early and late pulse, respectively.