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IET Quantum Communication

The impact of spot‐size on single‐photon avalanche diode timing‐jitter and quantum key distribution

Alexandra Lee, Alfonso Tello Castillo, Craig Whitehill, Ross J. Donaldson

Published Feb 26, 2024• 5 citations
Publisher

Abstract

Abstract In free‐space implementations of Quantum key distribution (QKD), the wide adoption of near‐Infrared wavelengths has led to the common use of silicon single‐photon avalanche diodes (Si‐SPAD) for receiver systems. While the impacts of some SPAD properties on QKD have been explored extensively, the relationship of spot‐size and spatial position on the full instrumental response and thus quantum bit error rate (QBER) has been studied little. Changes in spot size and spatial position can result from atmospheric turbulence and pointing and tracking errors. Here, An empirical analysis of that relationship is presented utilising a large active area, 500 μm, free‐space coupled Si‐SPAD designed for free‐space QKD. A baseline full‐width at half‐maximum timing jitter of 182 ps and a QBER contribution of 0.1 % for a 1 GHz clock frequency QKD system and 100 ps time‐gating window are reported. The impacts of spot‐size and spatial position can increase the QBER to over 0.3%. The link between the spot‐size and timing jitter will allow the understanding of tolerancing for the alignment of Si‐SPADs within free‐space QKD receiver systems—an important factor in designing properly engineered practical systems and the equipment needed to compensate for atmospheric turbulence and pointing and tracking.

DOI
10.1049/qtc2.12091

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The full time-jitter response of a single-photon detector can make a significant contribution to the quantum bit error rate (QBER) of high repetition rate quantum key distribution (QKD) implementations. Although there have been studies into understanding the contribution for single-mode optical fiber coupled single-photon detectors, the contribution of larger, multimode core diameters to the QBER have not been explored in detail. With the growing importance of free-space QKD, which typically use multimode fibers to reduce coupling loss, it is vitally important to understand how the multimode fiber coupling will impact the total QBER. This work studies the impact of the time-jitter contribution to QBER when coupling a commercial off-the-shelf silicon single-photon avalanche diode with various multimode fibers while simulating operating at 1 GHz with empirical measurements taken at 1 MHz repetition rate. It was found that step-index multimode fibers can significantly increase the QBER, while graded-index fibers can provide an QBER contribution similar to a single-mode fiber. The results highlight that there is a significant benefit in using graded index multimode fibers for a free-space QKD receiver, particularly for high repetition rate applications.
Experimental results obtained with silicon single photon avalanche diodes (SPADs) in quantum key distribution (QKD) at short wavelengths reveal remarkable potential for application in local area networks (LAN) and for free-space transmission at high rate. Actual application prospects, however, depend on the performance level and on the suitability of practical systems using the available silicon SPAD devices. They can be essentially divided in two groups: planar p-n junction structures with a thin depletion layer (typically 1 μm); and reach-through structures with a thick depletion layer (from 20 μm to 150μm). The physical mechanisms that control the device behaviour were investigated and the effect on the key parameters of the detector (quantum detection efficiency, dark counting rate, afterpulsing probability and photon-timing jitter) were thoroughly assessed. A quantitative analysis was made of the influence of such parameters on the quantum bit error rate (QBER). Actual parameters were measured and the attainable performance and system suitability of the two device types evaluated. Comparable performance is obtained, but from a system viewpoint thin SPADs appear inherently better suited to high-rate QKD applications, because of their faster response time, ruggedness, low voltage, low power dissipation and fabrication technology, which is simple, efficient, economical and compatible with monolithic integration of detector and associated circuits.
We discuss high-speed electronics that support the use of single-photon avalanche diodes (SPADs) in gigahertz singlephoton communications systems. For InGaAs/InP SPADs, recent work has demonstrated reduced afterpulsing and count rates approaching 500 MHz can be achieved with gigahertz periodic-gating techniques designed to minimize the total avalanche charge to less than 100 fC. We investigate afterpulsing in this regime and establish a connection to observations using more conventional techniques. For Si SPADs, we report the benefits of improved timing electronics that enhance the temporal resolution of Si SPADs used in a free-space quantum key distribution (QKD) system operating in the GHz regime. We establish that the effects of count-rate fluctuations induced by daytime turbulent scintillation are significantly reduced, benefitting the performance of the QKD system.
Quantum key distribution (QKD) can produce secure cryptographic key for use in symmetric cryptosystems. By adopting clock-recovery techniques from modern telecommunications practice we have demonstrated a free-space quantum key distribution system operating at a transmission rate of 625 MHz at 850 nm. The transmission rate of this system is ultimately limited by the timing resolution of the single-photon avalanche photodiodes (SPADs), and we present a solution to take advantage of SPADs with higher timing resolution that can enable repetition rates up to 2.5 GHz. We also show that with high-repetition-rate sub-clock gating these higher-resolution SPADs can reduce the system's exposure to solar background photons, thus reducing the quantum-bit error rate (QBER) and improving system performance.
Abstract In this paper, we analyze the performance of free-space optical quantum key distribution (FSO-QKD) using the BB84 protocol with BPSK modulation under realistic channel conditions. The Málaga distribution is employed to model the composite atmospheric turbulence, considering pointing errors. We derive closed-form expressions for the average quantum bit error rate (QBER) and the secure key rate (SKR), incorporating both turbulence and misalignment effects. Numerical results demonstrate the impact of turbulence parameters and beam misalignment on system performance. The findings provide insights for the robust design of FSO-QKD systems under practical deployment conditions.
This paper investigates the performance of satellite-based quantum key distribution (QKD) under realistic channel conditions, emphasizing the adverse effects of photon loss introduced by pointing errors and the presence of background photons. By leveraging a stochastic framework, we model the probability distribution of the number of photons detected at the receiver, considering Gaussian beam propagation, finite receiver aperture, and Poisson-distributed background noise. We then evaluate essential QKD performance metrics—such as the quantum key rate, quantum bit error rate (QBER), and outage probability—across a wide range of beam waist sizes and tracking accuracies. Numerical simulations demonstrate how subtle increases in the pointing error variance can drastically reduce the secure key generation rate, particularly for tightly focused beams. These findings highlight the importance of precise pointing systems and careful selection of optical parameters to ensure an acceptable QBER and a sufficiently high secret key rate in inter-satellite QKD links.