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arXiv:0706.1449 · New Journal of Physics

Detector dead-time effects and paralyzability in high-speed quantum key distribution

Daniel J. Rogers, Joshua C. Bienfang, Anastase Nakassis, Xu Hai, Charles W. Clark

Published Sep 10, 2007• 30 citations
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Abstract

Recent advances in quantum key distribution (QKD) have given rise to systems that operate at transmission periods significantly shorter than the dead times of their component single-photon detectors. As systems continue to increase in transmission rate, security concerns associated with detector dead times can limit the production rate of sifted bits. We present a model of high-speed QKD in this limit that identifies an optimum transmission rate for a system with given link loss and detector response characteristics.

DOI
10.1088/1367-2630/9/9/319

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Recent advances in quantum key distribution (QKD) have given rise to systems that operate at transmission periods significantly shorter than the dead times of their component single-photon detectors. As systems continue to increase in transmission rate, security concerns associated with detector dead times can limit the production rate of sifted bits. We present a model of high-speed QKD in this limit that identifies an optimum transmission rate for a system with given link loss and detector response characteristics.
Recently, there has been growing research interest in quantum technology in general and particularly in quantum key distribution (QKD) that enables two legitimate parties to share a secret key without leaking information to third parties. Practical implementation of QKD has shown limited key rates due to the practical limits of quantum sources and detectors. For example, after each detection event, practical single-photon detectors such as single-photon avalanche diodes (SPADs) undergo a period of inactivity called dead time, which limits the highest photon transmission rate achievable for QKD systems as photon transmission at sub-dead-time regime can generate security loopholes. In this paper, we analyze the performance of a sifting scheme that allows for high-speed operation at sub-dead-time regime both theoretically and numerically. We consider an FSO QKD system, where the effect of background noise can be significant and derive the expressions of sifting probability and sifted bit rate considering both dead time and background noise effects. We present a comprehensive performance analysis of the QKD system in terms of quantum bit error rate (QBER) and secrecy key rate (SKR) and show that operation at sub-dead-time regime can significantly improve the achievable SKR for FSO systems with certain path loss and background noise levels.
There has been growing research interest in quantum technology in general and in quantum key distribution (QKD) in particular. However, the key generation rate of QKD systems is still limited by the quantum channel losses as well as the practical limitations of the quantum sources and detectors. Here, we focus on one of these limitations, namely, the quantum detector's dead time effect, which happens after each photon detection, limiting the maximum quantum bit transmission rate and consequently the key generation rate of QKD systems. Qubit transmission at the sub-dead-time regime (i.e., faster than the reciprocal of dead time) can introduce different security loopholes. In this paper, we propose the use of a detector array instead of a single detector to measure the quantum state of individual photons in discrete variable QKD systems, showing that it can significantly alleviate the limitations induced by detectors' dead time. A dead-time compensated BB84 scheme is introduced, allowing qubit transmission at the sub-dead-time regime. AnM−M-M−dimensional Markov chain model is used to describe the impact of dead time on the operation of the proposed BB84 system, employing detector arrays of sizeMMM. Consequently, novel analytical expressions can be derived for the sifted bit rate (SBR) and secrecy key rate (SKR) of the proposed QKD system, showing excellent match with the Monte Carlo simulation results. A remarkable gain is observed for the BB84 system employing detector arrays, showing a potentialMMM-fold improvement of SBR at high qubit transmission rates.
The security of a high speed quantum key distribution system with finite detector dead time τ is analyzed. When the transmission rate becomes higher than the maximum count rate of the individual detectors (1/τ), security issues affect the algorithm for sifting bits. Analytical calculations and numerical simulations of the Bennett-Brassard BB84 protocol are performed. We study Rogers et al.'s protocol (introduced in "Detector dead-time effects and paralyzability in high-speed quantum key distribution," New J. Phys. 9 (2007) 319) in the presence of an active eavesdropper Eve who has the power to perform an intercept-resend attack. It is shown that Rogers et al.'s protocol is no longer secure. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are secure in the presence of dead time and an active eavesdropper are then introduced. We analyze and compare these secure sifting schemes for this active Eve scenario, and calculate and simulate their key generation rate. It is shown that the maximum key generation rate is 1/(2τ) for passive basis selection, and 1/τ for active basis selection. The security analysis for finite detector dead time is also extended to the decoy state BB84 protocol.
Quantum-key-distribution (QKD) protocols that rely on coincidence events registered with two or more detectors are prone to detector saturation effects due to detector dead times. In particular, systems using avalanche photodiodes may incur a reduction in the achievable secret key rate. We demonstrate a detector gating scheme tuned to mitigate these effects but keep the detectors in an otherwise free-running mode. When a first detector is inactive due to a previous detection, other unfavorable detection events in a second detector are blocked, as they would not contribute to the key but just lead to another dead time. We implement this method by synchronizing the detectors’ dead time in our time-bin entanglement QKD system and demonstrate its feasibility for various fiber link distances and detector settings, increasing the sifted key rate by up to 78% with no significant change in the quantum bit error rate.
The desire for quantum-generated cryptographic key for broadband encryption services has motivated the development of high-transmission-rate single-photon quantum key distribution (QKD) systems. The maximum operational transmission rate of a QKD system is ultimately limited by the timing resolution of the single-photon detectors and recent advances have enabled the demonstration of QKD systems operating at transmission rates well in to the GHz regime. We have demonstrated quantum generated one-time-pad encryption of a streaming video signal with high transmission rate QKD systems in both free-space and fiber. We present an overview of our high-speed QKD architecture that allows continuous operation of the QKD link, including error correction and privacy amplification, and increases the key-production rate by maximizing the transmission rate and minimizing the temporal gating on the single-photon channel. We also address count-rate concerns that arise at transmission rates that are orders of magnitude higher than the maximum count rate of the single-photon detectors.