Experimental Phase-Matching Quantum Cryptographic Conferencing in Symmetric and Asymmetric Fiber Channels

TL;DR

The paper addresses enabling secure multiparty quantum conferencing over long-distance fiber networks by extending the phase-matching QCC to a three-intensity scheme that accommodates asymmetric channels and finite-size effects. It combines frequency-locking and phase-tracking to synchronize three parties and provides security proofs via entanglement-based and source-replacement methods with a decoy-state analysis, yielding a key-rate formula $R=\left( \frac{2}{D} \right)^2 Q_{\mu} [1-f h(E^{max}_Z) - h(E^U_X)]$. Experiments demonstrate symmetric-channel secure transmission up to $100$ km per party (corresponding to $200$ km between parties) and show that, in asymmetric channels, per-party intensity optimization can significantly boost finite-size key rates without loss compensation. These results validate PM QCC as a feasible approach for intercity, star-type quantum networks and highlight its practical benefits for scalable multiparty quantum cryptography.

Abstract

Quantum cryptographic conferencing (QCC) allows multiple parties to establish common secure keys in quantum networks with information-theoretic security. However, the secure transmission distances of current QCC implementations are still limited to the metropolitan areas. Here, we experimentally demonstrate the three-intensity phase-matching (PM) QCC protocol considering finite-size effects by employing frequency-locking and phase-tracking techniques for three parties. The key distribution capability of the PM QCC protocol is demonstrated in the symmetric fiber channels with the distance from each party to the measurement site up to 100 km. The network adaptability of the PM QCC protocol is demonstrated in asymmetric fiber channels used to simulate fiber channel configurations in real networks. Thus, the feasibility of applying the PM QCC protocol to practical intercity quantum networks with both symmetric and asymmetric channels is verified.

Figures (8)

• Figure 1: Three parties in a star-type quantum network are conducting an encrypted conference using the common key generated by the QCC protocol. The relay can be an untrusted entanglement source or measurement site, and the distance from each party to the relay may be different.
• Figure 2: Experimental setup of PM QCC protocol for three parties. (a) Layout: Three parties Alice, Bob, and Charlie are connected to the measurement site (MS) through single-mode fiber (SMF). Bob and Charlie's continuous-wave lasers (CWLs) act as slave CWLs (SCWLs), frequency locked to Alice's master CWL (MCWL) using heterodyne optical phase-locked loop (OPLL) technology with acousto-optic modulator (AOM) enhancing feedback bandwidth. Alice then uses an AOM to align the frequency of remaining MCWL beam with those of Bob and Charlie. The three parties have the same encoder for intensity and phase modulation of coherent light pulses. At the MS, Alice's coherent state is split by beam splitter (BS) into two parts, which interfere with the coherent states of Bob and Charlie in the other two BS after passing through the polarisation feedback system (PFS). The interference results are then detected by four channels of superconducting nanowire single-photon detector (SNSPD). (b) Encoder: The encoder consists of an intensity modulator(IM), two Sagnac rings (SRs), two circulators (CIRs) in front of two SRs, a phase modulator (PM) between the two SRs, and a variable optical attenuator (VOA). A test port (TP) is reserved for each circulator. (c) Pulse: The encoder generates 62500 pulses per $100\us$ with 10 repeating regions excluding the pulses used for time calibration. Each repeating region consists of a reference pulse region, a vacuum region, and a signal pulse region. There are 2216 pulses in each reference pulse region and 4000 pulses in each signal pulse region. (d) PFS: The PFS is used to align the polarization of coherent light pulses. Each PFS is composed of an electric polarization controller (EPC), a polarization beamsplitter (PBS), and one channel of the detector.
• Figure 3: Key rates for symmetric fiber channels. The magenta solid line and cyan dash-dotted line represent the simulated asymptotic key rates and the key rates with total rounds of $N=10^{14}$ considering finite-size effects, respectively. The misalignment error $e_d=0.03$. The red asterisks and blue solid circles represent the experimental asymptotic key rates and key rates considering finite-size effects, respectively. The green diamonds and squares represent the experimental results of Refs. PRLYang2024 and PRLDu2025, respectively. For comparison, attenuation used in the experiment of Ref. PRLDu2025 are converted to fiber distances with the same attenuation. The error correction efficiency $f = 1.06$QIPTang2021. The failure probability of finite-size analysis $\epsilon=10^{-10}$.
• Figure 4: Key rates for asymmetric fiber channels. The black solid squares and magenta stems represent the experimental and simulated key rates, respectively. The total number of rounds $N=4\times10^{13}$ and the misalignment error $e_d=0.03$ for simulation. The secure key rate for symmetric fiber configurations of $\{75, 75, 75\}$ km are added for comparison.
• Figure 5: PM QCC protocol for three parties. Three parties Alice, Bob, and Charlie have the same device to prepare weak coherent state. They use lasers as coherent light sources and encoders to modulate the intensity and phase of coherent light pulses, thereby preparing the required coherent states $\ket{e^{\mathrm{i}\varphi_A}\sqrt{\mu_A}}$,$\ket{e^{\mathrm{i}\varphi_B}\sqrt{\mu_B}}$ and $\ket{e^{\mathrm{i}\varphi_C}\sqrt{\mu_C}}$. The coherent states prepared by the three parties are transmitted through fiber channels to the measurement site (MS). There, the coherent states prepared by Alice are split into two parts by beam splitter (BS), which interfere with the coherent states of Bob and Charlie, respectively, forming two measurement branches. The interference results of two branches are detected by four single-photon detectors (SPDs).