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arXiv:0909.5527 · New Journal of Physics

Boosting up quantum key distribution by learning statistics of practical single-photon sources

Yoritoshi Adachi, Takashi Yamamoto, Masato Koashi, Nobuyuki Imoto

Published Nov 17, 2009• 13 citations
arXivHTMLPDF

Abstract

We propose a simple quantum-key-distribution (QKD) scheme for practical single-photon sources (SPSs), which works even with a moderate suppression of the second-order correlation g (2) of the source. The scheme utilizes a passive preparation of a decoy state by monitoring a fraction of the signal via an additional beam splitter and a detector at the sender's side to monitor photon-number splitting attacks. We show that the achievable distance increases with the precision with which the sub-Poissonian tendency is confirmed in higher photon-number distribution of the source, rather than with actual suppression of the multiphoton emission events. We present an example of the secure key generation rate in the case of a poor SPS with g (2) =0.19, in which no secure key is produced with the conventional QKD scheme, and show that learning the photon-number distribution up to several numbers is sufficient for achieving almost the same distance as that of an ideal SPS.

DOI
10.1088/1367-2630/11/11/113033

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arXiv:quant-ph/0609195•Physical Review A•May 31, 2007•102 citations
We propose a simple quantum-key-distribution (QKD) scheme for practical single-photon sources (SPSs), which works even with a moderate suppression of the second-order correlation g (2) of the source. The scheme utilizes a passive preparation of a decoy state by monitoring a fraction of the signal via an additional beam splitter and a detector at the sender's side to monitor photon-number splitting attacks. We show that the achievable distance increases with the precision with which the sub-Poissonian tendency is confirmed in higher photon-number distribution of the source, rather than with actual suppression of the multiphoton emission events. We present an example of the secure key generation rate in the case of a poor SPS with g (2) =0.19, in which no secure key is produced with the conventional QKD scheme, and show that learning the photon-number distribution up to several numbers is sufficient for achieving almost the same distance as that of an ideal SPS.
Quantum key distribution (QKD) relies on single photon sources (SPSs), e.g. from solid-state systems, as flying qubits, where security strongly requires sub-Poissonian photon statistics with low second-order correlation values ($g^{(2)}(0)$). However, achieving such low $g^{(2)}(0)$ remains experimentally challenging. We therefore propose a decoy-like QKD protocol that relaxes this constraint while maintaining security. This enables the use of many SPSs with $g^{(2)}(0) > $0.1, routinely achieved in experiments but rarely considered viable for QKD. Monte Carlo simulations and our experiment from defects in hexagonal boron nitride show that, under linear loss, $g^{(2)}(0)$ remains constant, whereas photon-number-splitting (PNS) attacks introduce nonlinear effects that modify the measured $g^{(2)}(0)$ statistics. Exploiting this $g^{(2)}(0)$ variation as a diagnostic tool, our protocol detects PNS attacks analogously to decoy-state methods. Both single- and two-photon pulses consequently securely contribute to the secret key rate. Our protocol outperforms the Gottesman--Lo--Lutkenhaus--Preskill (GLLP) framework under high channel loss across various solid-state SPSs and is applicable to the satellite-based communication. Since $g^{(2)}(0)$ can be extracted from standard QKD experiments, no additional hardware is required. The relaxed $g^{(2)}(0)$ requirement simplifies the laser system for SPS generation. This establishes a practical route toward high-performance QKD without the need for ultra-pure SPSs.
The performance of a practical quantum key distribution (QKD) system is often limited by the multi-photon state emission of its source and the dark counts of its detectors. Here, we present two methods to improve its performance. The first method is decoy state QKD: the sender randomly sends out weak coherent states with various average photon numbers (which are named as signal state and decoy states). In [14,15], we have performed the first experimental implementation of decoy state QKD over 15km and 60km respectively, thus dramatically increasing the distance and secure key generation rate of practical QKD systems. Our work has been followed up by many research groups worldwide [16-18]. The second scheme is QKD with "dual detectors" [19]: the legitimate receiver randomly uses either a fast (but noisy) detector or a quiet (but slow) detector to measure the incoming quantum signals. The measurement results from the quiet detector can be used to upper bound the eavesdropper's information, while the measurement results from the fast detector are used to generate a secure key. We applied this idea to various QKD protocols. Simulation results demonstrated significant improvements in both BB84 protocol with ideal single photon source and Gaussian-modulated coherent states protocol.
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.
A passive scheme with a photon-number-resolving detector and a beam splitter which are used to monitor the statistical characteristics of photon source, is proposed to verify the security of three-intensity decoy-state quantum key distribution system with an untrusted source. The practical issues due to statistical fluctuation and detection noise are analyzed. The simulation results show that the scheme can work efficiently when the data size N≥108N\ge10^{8}N≥108 and the dark count rate of the detector is below 0.5 counts/pulse, which are realizable by current techniques. We also give an experimental example of PNR detector which is easily realized by a variable optical attenuator combined with a practical threshold detector.
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.
We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present day, nonideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical postprocessing. This allows one to improve the effective signal statistics and achievable distance.