Quantum communication complexity (QCC) explores the minimum communication needed for tasks using quantum states. Quantum fingerprinting (QF), a key example, allows exponentially less communication than classical methods. Existing coherent quantum fingerprinting (CQF) protocols, while demonstrating quantum advantages, suffer from communication time increasing quadratically with input size and sensitivity to detector dark counts, often requiring expensive superconducting-nanowire single photon detectors (SNSPDs) to achieve optimal performance. This research addresses these limitations by introducing a new protocol.

The paper reviews existing work in quantum communication, including quantum cryptography and quantum communication complexity. It highlights the exponential advantage of quantum fingerprinting over classical methods, referencing protocols and experimental demonstrations. The limitations of previous coherent quantum fingerprinting (CQF) protocols are discussed, particularly the quadratic increase in communication time and the reliance on low-dark-count SNSPDs to overcome limitations imposed by detector noise. The existing literature is used to set the stage for the proposed improvement leveraging wavelength-division multiplexing (WDM).

The researchers propose a Wavelength-Division Multiplexing Coherent Quantum Fingerprinting (WDM-CQF) protocol. In this protocol, Alice and Bob divide their coherent fingerprints into multiple subfingerprints, each assigned to a different wavelength channel. These subfingerprints are multiplexed into a single fiber and sent to Charlie. Crucially, demultiplexing is not needed at Charlie's end; simultaneous detection of all channels is performed. This reduces the mean photon number (μ) required for reliable discrimination, thereby decreasing the amount of communication. The theoretical model is detailed, including equations for the communication amount (Q), detection probabilities (PE and PD), and error probability (Perror). A proof-of-concept experiment is designed using six wavelength channels over a 40 km fiber, employing a Sagnac interferometer to stabilize phase fluctuations. The challenges of polarization mode dispersion in long fibers are addressed using polarization controllers and the principal state of polarization technique. Careful calibration ensures the simultaneous detection of all six wavelength channels.

The theoretical analysis shows that the WDM-CQF protocol consistently reduces communication time and the amount of communication by orders of magnitude as the number of channels (k) increases. Simulations demonstrate the protocol's ability to beat the classical limit even without SNSPDs for various distances (0 km, 40 km, and 80 km). The experimental results with six wavelength channels confirm the theoretical predictions. The WDM-CQF protocol consistently outperforms the best-known classical protocol and the original CQF protocol. For large input sizes, the experimental reduction in communication is more than half compared to the original CQF protocol. The experimental setup successfully addressed challenges such as wavelength-dependent polarization mode dispersion, maintaining high interference visibility (97%).

The results show a significant improvement in the efficiency of quantum fingerprinting, surpassing previous protocols and classical limits. The use of WDM and simultaneous detection reduces the amount of communication and allows the system to overcome limitations imposed by detector noise and channel losses, even without expensive SNSPDs. The experimental demonstration successfully validates the theoretical predictions, showcasing the practical feasibility of the WDM-CQF protocol. The approach of simultaneous detection of multiple bits of information is highlighted as a key element for improvement, applicable beyond the specific WDM implementation.

This paper presents a novel quantum fingerprinting protocol that significantly improves upon existing methods. By leveraging WDM and simultaneous detection, the protocol achieves substantial reductions in communication time and amount of communication. The experimental validation confirms its superiority over classical and previous quantum protocols. Future research could explore combining WDM with other multiplexing techniques to further optimize performance and investigate the applicability of this method to other quantum communication protocols.

The experimental demonstration uses only six wavelength channels, limiting the full potential of the WDM-CQF protocol. The current polarization alignment method may not be scalable to a much larger number of channels. Although the use of chromatic dispersion simplifies phase modulation, it does not allow for truly simultaneous modulation, affecting communication time reduction in the experiment. Further studies are needed to fully optimize the protocol and address scalability issues.