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Physical Review A

Finite-key interfering-or-not-interfering quantum key distribution without intensity modulation

Yue Li, Kaiyi Shi, Haoyang Wang, Chang Liu, Yujia Zhang, Duo Ma, Haiqiang Ma

Published Mar 10, 2025• 0 citations
Publisher

Abstract

This paper presents an enhanced interfering-or-not-interfering quantum key distribution (INI-QKD) protocol incorporating a scheme without intensity modulation (IM), which circumvents the impulse correlation issue associated with IM. Based on the minimum smooth entropy, we derive the key rate for finite code lengths and estimate the phase bit error rate using a no-decoy state method. Simulation results show that the protocol achieves the maximum communication distance of 337 km with quantum bit error rate of approximately $0.36%$. Moreover, the feasibility of using fewer phase plates ($M=6,8$) to realize discrete random phases in INI-QKD is also verified. Notably, the INI-QKD without IM exhibits significant advantages under polarization misalignment and phase mismatch conditions, reflecting greater adaptability to complex environments. By simplifying experimental setups and reducing the technical challenges, the INI-QKD without IM provides an alternative realization idea in the field of quantum communication.

DOI
10.1103/physreva.111.032608

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arXiv:1805.09222•Physical Review A•Dec 18, 2018•398 citations
This paper presents an enhanced interfering-or-not-interfering quantum key distribution (INI-QKD) protocol incorporating a scheme without intensity modulation (IM), which circumvents the impulse correlation issue associated with IM. Based on the minimum smooth entropy, we derive the key rate for finite code lengths and estimate the phase bit error rate using a no-decoy state method. Simulation results show that the protocol achieves the maximum communication distance of 337 km with quantum bit error rate of approximately 0.360.36%0.36. Moreover, the feasibility of using fewer phase plates (M=6,8M=6,8M=6,8) to realize discrete random phases in INI-QKD is also verified. Notably, the INI-QKD without IM exhibits significant advantages under polarization misalignment and phase mismatch conditions, reflecting greater adaptability to complex environments. By simplifying experimental setups and reducing the technical challenges, the INI-QKD without IM provides an alternative realization idea in the field of quantum communication.
Quantum key distribution provides a promising solution for sharing secure keys between two distant parties with unconditional security. Nevertheless, quantum key distribution is still severely threatened by the imperfections of devices. In particular, the classical pulse correlation threatens security when sending decoy states. To address this problem and simplify experimental requirements, we propose a phase-matching quantum key distribution protocol without intensity modulation. Instead of using decoy states, we propose an alternative method to estimate the theoretical upper bound on the phase error rate contributed by even-photon-number components. Simulation results show that the transmission distance of our protocol could reach 305 km in telecommunication fiber. Furthermore, we perform a proof-of-principle experiment to demonstrate the feasibility of our protocol, and the key rate reaches 22.5 bit/s under a 45-dB channel loss. Addressing the security loophole of pulse intensity correlation and replacing continuous random phase with a six- or eight-slice random phase, our protocol provides a promising solution for constructing quantum networks.
Single-photon interference is the essential key for the recently well-known twin-field quantum key distribution (TF-QKD) to break the linear rate-distance limit and requires beams with identical polarizations. Inspired by this fact and aiming to improve the secret key rate, we propose a hybrid high-dimensional QKD named the interfering-or-not-interfering QKD (INI-QKD), in which both the polarization and phase degrees of freedom (DOFs) are adopted as information carriers. The protocol's security proof is analyzed based on entanglement distillation and three defined effective events, X1{X}_{1}X1​, X2{X}_{2}X2​, and X3{X}_{3}X3​. The simulation shows that the X1{X}_{1}X1​ event, from which only the phase information is extracted, exceeds TF-QKD's variants, while the X2{X}_{2}X2​ and X3{X}_{3}X3​ events, in which both types of information are decoded, can achieve twice the secret key rate as measurement-device-independent QKD (MDI-QKD). It is also proven that by adding the polarization DOF, INI-QKD obtains more resistance to phase mismatch than TF-QKD. Remarkably, these can all be achieved by simply altering the TF-QKD's measurement setup to that of MDI-QKD.
The decoy-state method serves as a cornerstone for practical quantum key distribution (QKD) with inherent immunity to photon-number-splitting attacks. Leveraging optical injection locking, we propose a directly modulated light source with a scheme that simultaneously generates intensity- and phase-modulated signals without external modulators. Removing external modulators eliminates modulator-related side-channel vulnerabilities, fundamentally enhancing QKD security. Integrated into a high-speed phase-encoding BB84 system with optimized one-decoy protocol and finite-size analysis, our system achieves positive key rates up to 20 dB channel loss (100 km fiber) with commercial InGaAs single-photon detectors, reducing transmitter complexity while ensuring security for practical QKD applications.
Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number N=1012N=10^{12}N=1012 and the SKR closely approaches the asymptotic limit up to 250 km with N=1014N=10^{14}N=1014. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.
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.
Based on the novel idea of twin-field quantum key distribution [TF-QKD; Lucamarini et al., Nature (London) 557, 400 (2018)], we present a protocol named the ``sending or not sending TF-QKD'' protocol, which can tolerate large misalignment error. A revolutionary theoretical breakthrough in quantum communication, TF-QKD changes the channel-loss dependence of the key rate from linear to square root of channel transmittance. However, it demands the challenging technology of long-distance single-photon interference, and also, as stated in the original paper, the security proof was not finalized there due to the possible effects of the later announced phase information. Here we show by a concrete eavesdropping scheme that the later phase announcement does have important effects and the traditional formulas of the decoy-state method do not apply to the original protocol. We then present our ``sending or not sending'' protocol. Our protocol does not take postselection for the bits in ZZZ-basis (signal pulses), and hence the traditional decoy-state method directly applies and automatically resolves the issue of security proof. Most importantly, our protocol presents a negligibly small error rate in ZZZ-basis because it does not request any single-photon interference in this basis. Thus our protocol greatly improves the tolerable threshold of misalignment error in single-photon interference from the original a few percent to more than 4545%45. As shown numerically, our protocol exceeds a secure distance of 700, 600, 500, or 300 km even though the single-photon interference misalignment error rate is as large as 1515%, 25%, 35%15, or 4545%45.