This paper develops a theoretical model for source-side implementation security in practical decoy-state quantum key distribution (QKD). The research object is a weak-coherent-pulse transmitter in which the emitted mean photon number is affected not only by the selected decoy setting, but also by semiconductor-laser dynamics, electrical drive response, intensity-modulator memory, residual optical effects, and slow drift. The transmitter is described at two modelling levels. The first layer is a nonlinear continuous-time carrier-photon-phase model used to explain physical mechanisms. The second layer is a pulse-indexed validation surrogate obtained by sampling the emitted pulse train under a declared operating regime and stroboscopic extraction rule. This distinction avoids treating a local discrete model as a globally valid replacement for nonlinear gain-switched laser dynamics. The model maps the selected intensity sequence to the actual pulse mean photon number, defines an operational memory length, and introduces vacuum-safe deviation metrics, residual-correlation diagnostics, conditional intensity laws, and photon-number probability intervals. These quantities are explicitly distinguished from composable security parameters. The security interpretation is an assumption audit: if the emitted intensity or phase statistics are history dependent, the standard decoy-state reduction to setting-independent photon-number yields and error rates is no longer automatic. The proposed framework therefore does not claim a new complete QKD security proof; it identifies measurable source quantities that must be exported to an appropriate finite-key or imperfect-source proof. The result is a mathematically traceable bridge between transmitter dynamics, source validation, and implementation-security requirements for practical decoy-state QKD systems. The objective of this paper is to develop a mathematically traceable dynamic source-deviation model for practical decoy-state QKD transmitters and to show how transmitter memory affects the assumptions used in decoy-state security analysis.
This paper develops a theoretical model for source-side implementation security in practical decoy-state quantum key distribution (QKD). The research object is a weak-coherent-pulse transmitter in which the emitted mean photon number is affected not only by the selected decoy setting, but also by semiconductor-laser dynamics, electrical drive response, intensity-modulator memory, residual optical effects, and slow drift. The transmitter is described at two modelling levels. The first layer is a nonlinear continuous-time carrier-photon-phase model used to explain physical mechanisms. The second layer is a pulse-indexed validation surrogate obtained by sampling the emitted pulse train under a declared operating regime and stroboscopic extraction rule. This distinction avoids treating a local discrete model as a globally valid replacement for nonlinear gain-switched laser dynamics. The model maps the selected intensity sequence to the actual pulse mean photon number, defines an operational memory length, and introduces vacuum-safe deviation metrics, residual-correlation diagnostics, conditional intensity laws, and photon-number probability intervals. These quantities are explicitly distinguished from composable security parameters. The security interpretation is an assumption audit: if the emitted intensity or phase statistics are history dependent, the standard decoy-state reduction to setting-independent photon-number yields and error rates is no longer automatic. The proposed framework therefore does not claim a new complete QKD security proof; it identifies measurable source quantities that must be exported to an appropriate finite-key or imperfect-source proof. The result is a mathematically traceable bridge between transmitter dynamics, source validation, and implementation-security requirements for practical decoy-state QKD systems. The objective of this paper is to develop a mathematically traceable dynamic source-deviation model for practical decoy-state QKD transmitters and to show how transmitter memory affects the assumptions used in decoy-state security analysis.
The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics and idealized device models. Practical implementations, however, deviate from these models due to unavoidable device imperfections, and existing security proofs fall short of capturing the complexity of real-world systems. Here we introduce a versatile numerical finite-key security framework valid against general coherent attacks and applicable to a broad class of practical QKD setups. It accommodates most relevant imperfections at both transmitter and receiver, including non-independent-and-identically-distributed (non-IID) signals arising in high-speed QKD systems due to the limited bandwidth of optical modulators, while requiring only partial characterization of the apparatuses. We demonstrate the power of our framework by proving the security of a realistic decoy-state QKD implementation with laser sources, providing a practical route towards rigorous security certification of real-world QKD setups.
Quantum Key Distribution (QKD) offers information-theoretic security grounded in the laws of quantum mechanics rather than computational assumptions. While its theoretical foundations are robust, practical implementations necessarily deviate from the idealized models assumed in security analyses, opening the door to side-channel attacks and implementation loopholes. In particular, most research to date has focused on mitigating vulnerabilities in the measurement devices, leading to the development of Measurement-Device-Independent QKD (MDI-QKD) and Twin-Field QKD (TF-QKD), which effectively close all receiver-side loopholes. By contrast, the security of the source has remained less explored, despite being critical for the overall integrity of QKD systems. The goal of this thesis is to develop security proofs that explicitly account for realistic imperfections in QKD sources. Special emphasis is placed on three main aspects: correlations between emitted pulses that violate independence assumptions, imperfect phase randomization arising from practical modulation schemes, and leakage of internal settings through passive or active side channels. By formulating rigorous methods to analyze these imperfections, the work aims to provide a framework that enables practitioners to quantify and mitigate implementation risks systematically. Additionally, this thesis seeks to clarify under which conditions the commonly used decoy-state method remains secure, and to what extent source assumptions can be relaxed without compromising performance. This thesis aims to advance the understanding of how real-world deviations impact QKD security and to contribute to the development of protocols and devices. Ultimately, this work is motivated by the ambition to help bring QKD from a theoretically promising idea to a mature technology deployable with confidence in practical scenarios.
With the potential of quantum computers to compromise current public-key cryptosystems, Quantum Key Distribution (QKD), which is based on the physical laws of quantum mechanics, has garnered significant attention. However, while QKD security proofs typically assume ideal single-photon sources, realistic implementations rely on Weak Coherent Pulses (WCP) due to the difficulties associated with commercializing true single-photon sources. Unfortunately, the multi-photon components inherent in WCPs are vulnerable to Photon Number Splitting (PNS) attacks, which limits the secure transmission distance to a few tens of kilometers. This article introduces the Decoy State method, which effectively resolves this issue. Proposed by W.-Y. Hwang in 2003 and further advanced by H.-K. Lo and X.-B. Wang, this technique utilizes the random interleaving of pulses with different mean photon numbers during transmission. By doing so, it enables the accurate estimation of single-photon yield and error rates, thereby effectively detecting PNS attacks. Because it can be implemented using standard commercial lasers and intensity modulators, the Decoy State method has become the standard technology in most modern QKD systems. It serves as a core component for long-distance quantum communication, enabling major milestones reported recently. This article reviews the principles, mathematical analysis, and latest applications of the Decoy State method.
The decoy-state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-splitting attack based on our experimental data, and show that it compromises the system's security. Then, based on the work of Tamaki et al. [New J. Phys. 18, 065008 (2016)], we obtain two analytical formulas to estimate the yield and error rate of single-photon pulses when the signal and decoy states are distinguishable. The distinguishability reduces the secure key rate below that of a perfect decoy-state protocol. To mitigate this reduction, we propose to calibrate the transmittance of the receiver (Bob's) unit. We apply our method to three QKD systems and estimate their secure key rates.