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arXiv:2607.00600

Influence of laser chirp and interferometer delay and imbalance on the performance of a time-bin BB84 quantum key distribution system

Loïc Millet, Alberto Boaron, Rob Thew, Gianluca Boso

quant-phSubmitted Jul 1, 2026• Announced Jul 2, 2026• 0 citations
arXivHTMLPDF

Abstract

We investigate the effect of interferometer delay and imbalance on the performance of a BB84 time-bin quantum key distribution system. We simulate the impact of interference visibility on system performance and measure the visibility of a pair of interferometers as a function of their relative time delay and intensity imbalance. In addition, our analysis highlights the effect of laser chirp on system performance.

Journal reference
Appl. Phys. Lett. 28 July 2025; 127 (4): 044001
DOI
10.1063/5.0280232

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We investigate the effect of interferometer delay and imbalance on the performance of a BB84 time-bin quantum key distribution system. We simulate the impact of interference visibility on system performance and measure the visibility of a pair of interferometers as a function of their relative time delay and intensity imbalance. In addition, our analysis highlights the effect of laser chirp on system performance.
Phase-randomized light is one of the key assumptions in the security proof of the Bennett-Brassard 1984 (BB84) quantum-key-distribution (QKD) protocol using an attenuated laser. Though the assumption has been believed to be satisfied for conventional systems, it should be reexamined for current high-speed QKD systems. The phase correlation may be induced by the overlap of the optical pulses, the interval of which decreases as the clock frequency increases. The phase randomness was investigated experimentally by measuring the visibility of interference. An asymmetric Mach-Zehnder interferometer was used to observe the interference between adjacent pulses from a gain-switched distributed feedback laser diode driven at 10 GHz. Low visibility was observed when the minimum drive current was set far below the threshold, while interference emerged when the minimum drive current was close to the threshold. The theoretical evaluation on the impact of the imperfect phase randomization provides target values for the visibility to guarantee the phase randomness. The experimental and theoretical results show that secure implementation of decoy BB84 protocol is achievable even for the 10-GHz clock frequency by using the laser diode under proper operating conditions.
In this study, we demonstrate the possibility of realizing the quantum key distribution system by temporal coding of time-bin qubits that are prepared and measured using unbalanced Mach-Zehnder interferometers. We also show that, to exclude a clear a priori identification of time-bin qubits with equal bases, their encoding with the symbols 0 and 1 can be accomplished by delaying one of them by half the clock interval. The uniqueness of measurements of qutrits in this algorithm is shown to be based on the ability of quantum particles in β-states to interfere with the probability amplitudes at the ports of the system interferometers, as well as the absence of collisions of signaling states of the qutrits in adjacent clock intervals. We describe a method for controlling such collisions, including those that are based on qubits prepared from quasi-one-photon coherent laser states.
Abstract We report on the adaptation of a commercially available fiber-based quantum key distribution (QKD) system with phase-time encoding to free-space operation. The proposed approach minimizes architectural modifications by replacing the single-mode receiving interferometer with a free-space multi-mode delay interferometer, enabling efficient detection of spatially distorted quantum states typical for atmospheric channels. Several interferometer configurations are experimentally investigated, and a multi-mode Michelson interferometer with polarization routing is identified as the optimal solution in terms of interference visibility, loss, and alignment robustness. The impact of chromatic and modal dispersion on phase-time interference is analyzed and shown to be manageable under realistic system parameters. A laboratory QKD experiment demonstrates stable operation with a quantum bit error rate of about 4.5% and a secret key rate of hundreds of bits per second, confirming the feasibility of extending fiber-based QKD platforms to free-space links.
One of the key assumptions in the security proof of BB84 quantum key distribution (QKD) protocol with a weak coherent light source is that the phase of each pulse emitted from the source is random. If the phases correlated, an efficient eavesdropping method exists, and more sacrifice bits are necessary to guarantee the security of the protocol. The phase correlation between the adjacent pulses was examined experimentally, for the first time, by measuring the visibility of interference. An asymmetric Mach-Zehnder interferometer was used to observe the interference between adjacent pulses from a distributed feedback (DFB) laser diode driven by 10 GHz clock signal. Clear interference was observed when the DC bias current exceeds the laser threshold. This high visibility implies phase correlation between pulses. In contrast, only a low visibility, i.e. very weak phase correlation, was observed when the DC bias current was set far below the threshold. The phase correlation became stronger as the DC bias current increased. The experimental results imply that a QKD equipment implementing BB84 protocol with a coherent light source is secure as long as the laser is operated in gain-switch even for 10 GHz clock frequency.
We present a design for a quantum key distribution (QKD) system in a Sagnac loop configuration, employing a novel phase modulation scheme based on frequency shift, and demonstrate stable BB84 QKD operation with high interference visibility and low quantum bit error rate (QBER). The phase modulation is achieved by sending two light pulses with a fixed time delay (or a fixed optical path delay) through a frequency shift element and by modulating the amount of frequency shift. The relative phase between two light pulses upon leaving the frequency-shift element is determined by both the time delay (or the optical path delay) and the frequency shift, and can therefore be controlled by varying the amount of frequency shift. To demonstrate its operation, we used an acousto-optic modulator (AOM) as the frequency-shift element, and vary the driving frequency of the AOM to encode phase information. The interference visibility for a 40 km and a 10 km fiber loop is 96% and 99%, respectively, at single photon level. We ran BB84 protocol in a 40-km Sagnac loop setup continuously for one hour and the measured QBER remained within the 2%-5% range. A further advantage of our scheme is that both phase and amplitude modulation can be achieved simultaneously by frequency and amplitude modulation of the AOM's driving signal, allowing our QKD system the capability of implementing other protocols, such as the decoy-state QKD and the continuous-variable QKD. We also briefly discuss a new type of Eavesdropping strategy ("phase-remapping" attack) in bidirectional QKD system
One of the key assumptions in the security proof of BB84 quantum key distribution (QKD) protocol with a weak coherent light source is that the phase of each pulse emitted from the source is random. If the phases correlated, an efficient eavesdropping method exists, and more sacrifice bits are necessary to guarantee the security of the protocol. The phase correlation between the adjacent pulses was examined experimentally, for the first time, by measuring the visibility of interference. An asymmetric Mach-Zehnder interferometer was used to observe the interference between adjacent pulses from a distributed feedback (DFB) laser diode driven by 10 GHz clock signal. Clear interference was observed when the DC bias current exceeds the laser threshold. This high visibility implies phase correlation between pulses. In contrast, only a low visibility, i.e. very weak phase correlation, was observed when the DC bias current was set far below the threshold. The phase correlation became stronger as the DC bias current increased. The experimental results imply that a QKD equipment implementing BB84 protocol with a coherent light source is secure as long as the laser is operated in gain-switch even for 10 GHz clock frequency.