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Communications in Theoretical Physics

Quantum digital signature with reference misalignment

Xin Sun, Yuxiang Bian, Yining Mao, Chao Lv, Jia Feng, Hua-Jian Ding

Published Nov 28, 2025• 0 citations
Publisher

Abstract

Abstract Quantum digital signature (QDS) ensures the authenticity, integrity, and non-repudiation of message transmission with information-theoretic security. However, most existing QDS protocols require users to maintain aligned reference frames, which is a complex and time-consuming process, especially in large-scale networks. To overcome this limitation, we propose a reference-frame-independent (RFI)-QDS protocol that eliminates the need for reference frame alignment by utilizing an RFI quantum key distribution technique. Our RFI-QDS protocol enhances signature rates and robustness by bypassing the reference calibration step. This advantage becomes particularly significant under conditions of large reference misalignment. Simulation results demonstrate that our protocol achieves significantly higher signature rates compared to traditional QDS schemes, even in the presence of severe reference misalignment.

DOI
10.1088/1572-9494/ae2580

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Abstract Quantum digital signature (QDS) ensures the authenticity, integrity, and non-repudiation of message transmission with information-theoretic security. However, most existing QDS protocols require users to maintain aligned reference frames, which is a complex and time-consuming process, especially in large-scale networks. To overcome this limitation, we propose a reference-frame-independent (RFI)-QDS protocol that eliminates the need for reference frame alignment by utilizing an RFI quantum key distribution technique. Our RFI-QDS protocol enhances signature rates and robustness by bypassing the reference calibration step. This advantage becomes particularly significant under conditions of large reference misalignment. Simulation results demonstrate that our protocol achieves significantly higher signature rates compared to traditional QDS schemes, even in the presence of severe reference misalignment.
Quantum digital signatures (QDS) exploit quantum laws to guarantee non-repudiation, unforgeability and transferability of messages with information-theoretic security. Current QDS protocols face two major restrictions, including the requirement of the symmetrization step with additional secure classical channels and the quadratic scaling of the signature rate with the probability of detection events. Here, we present an efficient QDS protocol to overcome these issues by utilizing the classical post-processing operation called post-matching method. Our protocol does not need the symmetrization step, and the signature rate scales linearly with the probability of detection events. Simulation results show that the signature rate is three orders of magnitude higher than the original protocol in a 100-km-long fiber. This protocol is compatible with existing quantum communication infrastructure, therefore we anticipate that it will play a significant role in providing digital signatures with unconditional security.
Reference-frame-independent quantum key distribution (RFI QKD) significantly alleviates alignment requirements for reference frame in practical quantum communication systems. While the original protocol requires Alice to prepare six quantum states in ZZZ, XXX, and YYY bases, its reliance on active modulation introduces inherent side-channel vulnerabilities from device imperfections. We address this security limitation by integrating a fully passive source into the RFI framework. In this paper, we propose a fully passive RFI QKD protocol. Our protocol avoids active modulation entirely, suppressing side-channel risks through passive quantum state generation. Moreover, by making full utilization of the quantum states generated by the fully passive source, we enhance the secure key rate of fully passive protocol. We establish a system model to analyze the performance of the protocol. Through the optimization of post-selection intervals and intensities, we obtain the maximum secure key transmission rate of the protocol. Under ideal circumstances, the secure key transmission rate of our protocol can reach more than 50% of that of the ideal QKD. Under practical conditions, we have considered the finite-length effect. When pulse number generated by the source reaches 101210^{12}1012, the maximum communication distances of the protocol can reach 167 km and 136 km with a reference frame misalignment of $0 $ and $45^{\circ} $ respectively. We believe that our protocol can contribute to the development of practical QKD systems.
Current quantum secure direct communication (QSDC) protocols guarantee communication security by estimating the error rates of photons in the X and Z bases. This take the reference frame calibration between communicating parties as a necessary prerequisite. However, in mobile communications scenarios, achieving continuous and accurate reference frame calibration poses significant challenges. To address this issue, this paper proposes a reference-frame-independent (RFI) QSDC protocol. This protocol only requires ensuring the calibration accuracy of one direction of the reference frame, while allowing a misalignment angle βββ in the other two directions. To improve the protocol's robustness against reference frame fluctuations, we introduce a βββ-independent parameter C into the security analysis framework and rederive the protocol's security bounds. Additionally, we construct a system model and optimize the pulse intensity of the signal states, enabling the protocol to achieve optimal performance under each level of channel attenuation. At an attenuation of 10 dB (corresponding to a communication distance of 25 km), the secrecy message capacities for $β= 0^{ \circ} $ and $45^{ \circ} $ are 8.765×10−68.765 \times10^{-6}8.765×10−6 bit/pulse and 4.150×10−64.150 \times10^{-6}4.150×10−6 bit/pulse, respectively. Compared with the single-photon-based QSDC, the communication distance of the protocol proposed in this paper is significantly extended. When $β= 0^{ \circ} $ and $45^{ \circ} $, the maximum transmission distances of the RFI QSDC protocol are 27.875 km and 26.750 km, which is about 155.9 % and 149.7 % of that of the single-photon-based QSDC protocol.
In secure communication, reference-frame calibration is critical to ensuring a secure key rate in quantum key distribution (QKD) systems. This process also increases the complexity of the system, which is not conducive to practical use. Although the reference-frame-independent (RFI) QKD protocol can simplify alignment, it requires three bases to prepare six states. Here the authors present instead a three-state RFI QKD protocol, and verify its security using a recently developed proof based on semidefinite programming. A proof-of-principle experiment is conducted to demonstrate the feasibility of the scheme. This work is sure to boost the practical application of the RFI QKD protocol.
The reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) protocol is immune to both the slow drift of the reference frame and the potential attacks aimed at the measurement device. However, its reference-frame-independent behavior in terms of performance relies on the assumption that the key-generation basis is well aligned, which may not always be satisfied in practice. In this work, to address this limitation in RFI-MDI-QKD, we propose a fully RFI-MDI-QKD (FRFI-MDI-QKD) protocol by harnessing the quantum discord resource, and prove its security against collective attacks in the asymptotic case. With a 3 × 3 matrix whose singular values are independent of the reference frame, the information obtained by the eavesdropper in FRFI-MDI-QKD is completely irrelevant to the reference frame. Simulation results show that, in the case of a misaligned key-generation basis, FRFI-MDI-QKD can yield more positive keys compared with previous RFI-MDI-QKD; in the case of a well-calibrated key-generation basis, the key rate performance of FRFI-MDI-QKD can be reduced to that of previous RFI-MDI-QKD.
Reference-frame-independent (RFI) quantum key distribution (QKD) removes the need to actively align Alice and Bob's bases, but existing security proofs and decoy-state treatments are either numerically heavy or overly pessimistic in realistic scenarios. In this work, we revisit the RFI QKD security proof, demonstrating that the protocol is subject to the same constraints as the standard six-state or BB84 protocol, thereby improving its robustness and performance. We then introduce a one-decoy finite-key analysis based on RFI-invariant correlators and virtual quantum bit error rates. Simulations show that our decoy method restores reference frame independent performance and yields higher secret-key rates than the original RFI analysis with three intensities, while simplifying the experimental setup by requiring only two intensity levels.