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

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

Problem Statement
Quantum cryptographic conferencing (QCC) enables multiple parties to establish a common secure key with information-theoretic security. While existing implementations have demonstrated QCC, their secure transmission distances are currently limited to metropolitan areas. Furthermore, most protocols assume symmetric fiber channels, whereas real-world networks often exhibit asymmetric channel configurations. Existing phase-matching (PM) QCC protocols, while offering improved key rates scaling from $O(\eta^M)$ to $O(\eta^{M-1})$ (where $\eta$ is transmittance and $M$ is the number of parties), originally required symmetric channels or loss compensation methods to function in asymmetric settings. Additionally, practical implementations must account for finite-size effects, which significantly impact key rates and security proofs in real-world scenarios.

Methodology
The authors experimentally demonstrate a three-intensity phase-matching (PM) QCC protocol for three parties (Alice, Bob, and Charlie) over both symmetric and asymmetric fiber channels.

• Protocol Refinement: The study extends the security proof of the original PM QCC protocol to asymmetric channels. Instead of compensating for channel loss, the protocol optimizes the transmitted light intensity of each party. The protocol utilizes a three-intensity scheme (one signal state and two decoy states) to simplify intensity modulation.
• Experimental Setup:
  • Frequency Locking: To establish a stable phase reference, Alice's continuous-wave laser (CWL) acts as a master source. Bob and Charlie lock their slave CWLs to Alice's frequency using heterodyne optical phase-locked loop (OPLL) technology enhanced by acousto-optic modulators (AOMs) to increase feedback bandwidth.
  • Phase Tracking: Due to fiber disturbances and imperfect locking, phase drift occurs. The system employs phase reference pulses to track drift ($\Delta\theta$) every 100 $\mu$s, allowing for real-time phase compensation.
  • Measurement: The untrusted measurement site (Eve) splits Alice's coherent state to interfere with Bob's and Charlie's states in two separate branches. Successful detection events are recorded by four superconducting nanowire single-photon detectors (SNSPDs).
  • Finite-Size Analysis: The experiment incorporates finite-size effects using the Chernoff-Hoeffding method to estimate bounds on gains and the upper bound of the phase error rate ($E^U_X$).

Key Contributions

1. Asymmetric Channel Adaptation: The paper successfully extends the PM QCC security proof to asymmetric channels. It demonstrates that by optimizing the intensity ratios of signal and decoy states for each party based on channel loss, the protocol can operate effectively without active loss compensation.
2. Three-Intensity Scheme: The protocol is refined into a three-intensity scheme, which simplifies the intensity modulation requirements compared to previous multi-intensity approaches.
3. Finite-Size Implementation: The experiment explicitly considers finite-size effects, providing a realistic assessment of key rates for practical network deployments rather than relying solely on asymptotic limits.
4. Frequency and Phase Stabilization: The implementation details a robust frequency-locking and phase-tracking mechanism essential for maintaining coherence among three independent parties over long distances.

Results

• Symmetric Channels: The protocol was tested in symmetric fiber configurations with distances from each party to the measurement site ranging from 25 km to 100 km.
  • Secure key distribution was achieved up to 100 km from each party to the measurement site (equivalent to a 200 km distance between two parties).
  • At 100 km, the experiment achieved a key rate of $4.20 \times 10^{-11}$ bits/pulse considering finite-size effects, with a total number of rounds ($N$) of $1.28 \times 10^{14}$.
  • The results show a significant improvement in secure transmission distance and key rate compared to previous polarization-encoded MDI-QCC implementations.
• Asymmetric Channels: The protocol was tested in five asymmetric configurations (e.g., {75, 25, 25} km, {75, 50, 50} km).
  • The optimized intensity scheme allowed for secure key generation in these configurations without loss compensation.
  • Notably, the asymmetric configuration {75, 25, 25} km achieved a key rate 5 times higher than the symmetric {75, 75, 75} km configuration, demonstrating the efficiency of the intensity optimization strategy.
• Limitations: The authors note that for distances exceeding 100 km, the implementation is severely limited by finite-size effects, as the gap between finite-size and asymptotic key rates increases significantly even with large $N$ ($>10^{14}$).

Significance
The paper claims to verify the feasibility of applying the PM QCC protocol to practical intercity quantum networks. By demonstrating secure key distribution over 100 km in symmetric channels and achieving higher key rates in asymmetric channels without loss compensation, the work extends the secure transmission distance of QCC from metropolitan to intercity scales. The authors state that these results promote the application of QCC protocols in real quantum networks, particularly star-type topologies, and provide a solid validation for implementing such protocols in environments with both symmetric and asymmetric channel characteristics.