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Iraqi Journal of Laser

Estimation of mean photon number based on single photon detection of weak coherent pulses

Hawraa A. Ghanem, Shelan Khasro Tawfeeq

Published Jun 15, 2025• 0 citations
Publisher

Abstract

The demand for single photon sources in quantum key distribution (QKD) systems has necessitated the use of weak coherent pulses (WCPs) characterized by a Poissonian distribution. Ensuring security against eavesdropping attacks requires keeping the mean photon number (µ) small and known to legitimate partners. However, accurately determining µ poses challenges due to discrepancies between theoretical calculations and practical implementation. This paper introduces two experiments. The first experiment involves theoretical calculations of µ using several filters to generate the WCPs. The second experiment utilizes a variable attenuator to generate the WCPs, and the value of µ was estimated from the photons detected by the BB84 detection setup. The second experiment represents an accurate method for estimating the value of µ because of using single photon detectors with high timing resolution and low dark counts, in addition to using a Time-to-digital convertor with a bin size of 81 ps.

DOI
10.31900/ijl.v23i1.455

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EPJ Web of Conferences•Jan 1, 2026•0 citations
The demand for single photon sources in quantum key distribution (QKD) systems has necessitated the use of weak coherent pulses (WCPs) characterized by a Poissonian distribution. Ensuring security against eavesdropping attacks requires keeping the mean photon number (µ) small and known to legitimate partners. However, accurately determining µ poses challenges due to discrepancies between theoretical calculations and practical implementation. This paper introduces two experiments. The first experiment involves theoretical calculations of µ using several filters to generate the WCPs. The second experiment utilizes a variable attenuator to generate the WCPs, and the value of µ was estimated from the photons detected by the BB84 detection setup. The second experiment represents an accurate method for estimating the value of µ because of using single photon detectors with high timing resolution and low dark counts, in addition to using a Time-to-digital convertor with a bin size of 81 ps.
Single photon source is indispensable for realization of photon based quantum communication technologies such as quantum key distribution (QKD). Weak coherent pulse source is a practical, efficient and robust solution to generate stream of single photons, probabilistically. In this paper, a methodology for design and development of weak coherent pulse (WCP) source with high count rate of upto 10 Mcps is proposed and implemented. The generation of optical pulses with narrow pulse width and repetition rate of up to 100 MHz is achieved by developing a miniaturized pulse laser module. The weak coherent pulses are generated by heavily attenuating the laser pulses so as to reach the mean photon no. per pulse, μ, close to 0.1. WCP source performance in terms of mean photon number, second order coherence and photon count rate is also investigated. The measured g(2)[0] of ~0.98 shows that the developed WCP source has a very good quality.
Key distribution system using faint laser is very likely to become the first application exploiting the particular properties of single quanta called photons. In experimental key distribution system, it is highly demanded to use single-photon source for secure key distribution. Since there is not yet a laser source capable of producing such faint state, most experiments uses low coherent pulse laser, which is attenuated to produce a mean photon number mu. In this paper, we present an experimental setup to determine the mean photon number using a 300-ps low coherent pulse laser at 1550 nm for a practical crypto system. We will also present the effect of trigger frequency, detection efficiency and dark counts on average photon counts.
Advancements in practical single-photon sources (SPS) exhibiting high brightness and low g(2)(0)g^{(2)}(0)g(2)(0) have garnered significant interest for their application in quantum key distribution (QKD). To assess their QKD performance, it is essential to compare them with the widely employed weak coherent pulses (WCPs) in the decoy state method. In this work, we analyze the non-decoy efficient BB84 protocol for an SPS, partially characterising its photon statistics by its g(2)(0)g^{(2)}(0)g(2)(0) and mean photon number. We compare it to the 2-decoy efficient BB84 with WCPs within the finite-key analysis framework while optimizing the parameters of both protocols. Our findings indicate that the non-decoy SPS with a mean photon number of ⟨n⟩=0.5\langle n \rangle = 0.5⟨n⟩=0.5 and g(2)(0)=3.6%g^{(2)}(0) = 3.6\%g(2)(0)=3.6% can enhance the secure key generation over the 2-decoy WCP for block sizes under 4.66⋅1094.66 \cdot 10^94.66⋅109 sent signals (292929 seconds of acquisition time) at a channel loss of 101010 dB (52.552.552.5 km of optical fibre). Additionally, we demonstrate an increase in the maximum tolerable channel loss for SPSs with mean photon number ⟨n⟩≥0.0142\langle n \rangle \geq 0.0142⟨n⟩≥0.0142 at block sizes below 10810^8108 sent signals (0.620.620.62 seconds of acquisition time). These results suggest that SPSs hold potential for key rate enhancement in short-range QKD networks, though further research is required to evaluate their key generation capabilities when integrated into the decoy method.
Quantum key distribution (QKD) theoretically offers unconditional security. Unfortunately, the gap between theory and practice threatens side-channel attacks on practical QKD systems. Many well-known QKD protocols use weak coherent laser pulses to encode the quantum information. These sources differ from ideal single photon sources and follow Poisson statistics. Many protocols, such as decoy state and coincidence detection protocols, rely on monitoring the photon statistics to detect any information leakage. The accurate measurement and characterization of photon statistics enable the detection of adversarial attacks and the estimation of secure key rates, strengthening the overall security of the QKD system. We have rigorously characterized our source to estimate the mean photon number employing multiple detectors for comparison against measurements made with a single detector. Furthermore, we have also studied intensity fluctuations to help identify and mitigate any potential information leakage due to state preparation flaws. We aim to bridge the gap between theory and practice to achieve information-theoretic security.
Quantum key distribution (QKD) allows two distant parties to share a secret key and realizes a communication with information-theoretic security by combining it with one-time-pad encryption.Since the Bennett-Brassard 1984 (BB84) protocol was proposed, a large number of researches on QKD have been conducted from both aspects of theory and implementations.For implementations of QKD, weak coherent pulses (WCP) are heavily used as optical signals because they are easily generated by typical lasers and attenuators.The security for QKD with WCP has been also studied along the development of the implementations.In this thesis, the security analysis of the QKD with WCP is considered and further developed from two aspects.First, the security of the differential-quadrature-phase-shift (DQPS) protocol is proved.The DQPS protocol has essentially the same set up as the phase-encoding BB84 (PE-BB84) protocol, which is one of the most frequently demonstrated protocols.Since the known proof techniques for the BB84 protocol is not directly applicable, a modified approach is developed which is suitable for the DQPS protocol.As a result, the advantage of the DQPS protocol in the key generation rate over the PE-BB84 protocol is shown in the asymptotic limit where the size of communication data is assumed to be infinite.Second, a new method for security analysis with finite-key size is proposed as a suitable method for QKD protocols using WCP.Differently from the current method based on simple random sampling, the proposed method relies on Bernoulli sampling, which is associated with binomial distribution.The security of the BB84 protocol is proved by using the Bernoulli-sampling method, enabling a simpler analysis with a smaller number of parameters to be estimated compared to the method with simple random sampling.The required number of detected signals to generate a secret key is shown to be smaller than 10 4 , which is drastic improvement from the number ∼ 10 7 obtained in the previous result.The proposed method is also applied to the DQPS protocol, and its advantage over the PE-BB84 protocol is certified even in the finite-key regime.i
For a start, Quantum Key Distribution offers security not depending on any fundamental assumption. However, actual realizations choose to use weak coherent pulses as photon sources, rather than the ideal single-photon state, which bears security weaknesses due to the emission of sporadic multi-photon states. These states can be used in Photon-Number Splitting (PNS) attacks, where the attacker intercepts and buffers photons of multi-photon pulses and forwards the rest, enabling partial recovery of the key without inducing detectable perturbations. This article presents a simulation-based approach to analyze PNS attacks with realistic channel conditions like losses, detector imperfections, and finite key lengths. The research also examines the performance of decoy-state countermeasures, that use variable-intensity pulses to statistically reveal eavesdropping and Simulation results confirm the dominant character of PNS on raw key rates for the no-countermeasure scenario and ensure optimal decoy-state schemes restore security by cutting single-photon contributions. Results establish that although WCP QKD is vulnerable to PNS attacks in theory, strict adoption of decoy-state protocols aided with monitoring and finite-key analysis can provide immunity against an adversary. The paper emphasizes the need for simulation-based, implementation-dependent security analysis in direction towards well-designed practical quantum cryptographic systems. [1] [2] [3] [4] [10] [8]