High-rate quantum digital signatures over 250 km of optical fiber

Abstract

Quantum digital signatures (QDS) offer information-theoretic security for message integrity, authenticity, and non-repudiation, and constitute a fundamental cryptographic primitive for future quantum networks. Despite significant progress, the practical deployment of QDS has been severely constrained by limited signature rates and poor tolerance to channel loss, particularly in long-distance and metropolitan-scale networks. Here, we report a high-rate, loss-resilient QDS system that overcomes these two key bottlenecks simultaneously. Our implementation combines intrinsically phase-stable polarization modulation based on a Sagnac interferometer with gigahertz-rate quantum state encoding and low-timing-jitter superconducting nanowire single-photon detectors, enabling robust and continuous operation at high repetition frequencies. By integrating this hardware platform with a one-time universal hashing-based QDS protocol, we achieve a signature rate improvement of more than two orders of magnitude compared with existing QDS implementations under comparable channel-loss conditions. Notably, the system maintains a non-zero effective signature rate of approximately 1.25 times per second at a total channel loss of up to 49.05 dB, representing the highest loss tolerance reported for QDS to date. These results establish a practical and scalable technological pathway for deploying QDS in real-world quantum communication networks.

Figures (4)

• Figure 1: Schematic of the OTUH-QDS protocol. The protocol consists of two stages: the distribution stage and the messaging stage, involving three parties: Alice (Signer), Bob (Receiver), and Charlie (Verifier). In the distribution stage, Bob and Charlie independently perform the one-decoy-state BB84 QKD protocol with Alice to generate correlated key strings $K_b$ and $K_c$. Alice then computes her secret key $K_a = K_b \oplus K_c$, establishing the three-party key correlations $X_a = X_b \oplus X_c$ and $Y_a = Y_b \oplus Y_c$. In the messaging stage, Alice signs an $m$-bit document $\mathrm{Doc}$: she first computes the hash value $\mathit{Hash} = H_{n \times m} \cdot \mathit{Doc}$, concatenates it with a random bit string $p_a$ to form the digest $\mathit{Dig} = (\mathit{Hash} \,\|\, p_a)$, and encrypts it with her key $Y_a$ to produce the signature $\mathit{Sig} = (\mathit{Dig} \oplus Y_a)$. The signature and document $\{\mathit{Sig}, \mathit{Doc}\}$ are then sent to Bob. Bob forwards the message to Charlie and exchanges keys with him. Bob (Charlie) uses the reconstructed keys $KY_b$ and $KX_b$ ($KY_c$ and $KX_c$) to decrypt the signature, obtaining the expected digest $\mathit{Dig}_b$ ($\mathit{Dig}_c$), and independently computes the actual digest $\mathit{Dig}_b'$ ($\mathit{Dig}_c'$) via hashing. The signature is accepted as valid if and only if both Bob and Charlie verify the equality $\mathit{Dig}_b = \mathit{Dig}_b'$ and $\mathit{Dig}_c = \mathit{Dig}_c'$.
• Figure 2: Schematic of the experimental setup of the QDS system. The system consists of two independent transmitters (Bob and Charlie) and one receiver (Alice), with all nodes interconnected by commercial standard single-mode fibers. Each transmitter (Bob/Charlie) comprises control computer, FPGA board (Electronics I/O), laser diode (LD), phase modulator (PM), beam splitter (BS), polarization beam splitter (PBS), variable optical attenuator (VOA), and dispersion compensation module (DCM), which together enable quantum-state preparation, encoding, and transmission. The receiver (Alice) includes polarization controller (PC), polarization analysis module (PAM), superconducting-nanowire single-photon detector (SNSPD), time-to-digital converter (TDC), and computer for quantum-state measurement and data acquisition. Optical modules are interconnected via single-mode fiber (SMF) and polarization-maintaining fiber (PMF), while electrical signals are delivered through RF lines. The mechanical optical switch (MOS) is shown only for clarity of the system architecture and is not present in the actual experiment.
• Figure 3: Electrical and optical signals for high-speed quantum-state preparation at a 1.25GHz repetition rate. All signals are recorded using a 25GHz-bandwidth oscilloscope. (a) Laser drive electrical signal. This signal is generated by a self-developed FPGA board, with a repetition rate of 1.25GHz and a pulse width of approximately 200ps, and is used for gain-switching operation of a DFB semiconductor laser; (b) Output optical pulse from the laser. The pulse is produced by gain-switching the DFB laser driven by the electrical signal in (a), exhibiting an FWHM of approximately 30ps. It is measured by a high-speed photodiode with 20GHz bandwidth; (c) Intensity modulator drive electrical signal. This signal is used for preparing signal and decoy states, with a pulse width of about 200ps. The waveform shown here is after 6dB broadband attenuation; (d) Polarization modulator drive electrical signal. This signal is employed for encoding the four polarization states ($|H\rangle$, $|V\rangle$, $|D\rangle$, $|A\rangle$) of the BB84 protocol by switching among four distinct voltage levels. Its pulse width is 200ps. The displayed signal is after 6dB broadband attenuation.
• Figure 4: Signature rates with different transmission loss. The blue solid line shows the theoretical simulation results obtained from the experimental system parameters, while the red pentagrams denote the signature rates achieved in this work over commercial standard single-mode fiber at 75 km, 100 km, 150 km, 200 km and 250 km. The circles correspond to the signature rate results from state-of-the-art QDS experiments (blue circle roberts2017experimental, orange circle an2018practical, green circle ding2020280, purple circle richter2021agile, yellow circle yin2023experimental, pink circle du2025chip, black circle lu2025fully, and gray circle lu2025fully), where data points from the same reference under different channel losses are connected by dashed lines.