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Experimental study of high speed polarization-coding quantum key distribution with sifted-key rates over Mbit/s

Xiao Hong Tang, Lijun Ma, Alan Mink, Anastase Nakassis, Xu Hai, Barry Hershman, Joshua C. Bienfang, David Su, Ronald F. Boisvert, Charles W. Clark, Carl J. Williams

Published Jan 1, 2006• 43 citations
Publisher

Abstract

We present a quantitative study of various limitations on quantum cryptographic systems operating with sifted-key rates over Mbit/s. The dead time of silicon APDs not only limits the sifted-key rate but also causes correlation between the neighboring key bits. In addition to the well-known count-rate dependent timing jitter in avalanche photo-diode (APD), the faint laser sources, the vertical cavity surface emission lasers (VCSELs) in our system, also induce a significant amount of data-dependent timing jitter. Both the dead time and the data-dependent timing jitter are major limiting factors in designing QKD systems with sifted-key rates beyond Mbit/s.

DOI
10.1364/oe.14.002062

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We present a quantitative study of various limitations on quantum cryptographic systems operating with sifted-key rates over Mbit/s. The dead time of silicon APDs not only limits the sifted-key rate but also causes correlation between the neighboring key bits. In addition to the well-known count-rate dependent timing jitter in avalanche photo-diode (APD), the faint laser sources, the vertical cavity surface emission lasers (VCSELs) in our system, also induce a significant amount of data-dependent timing jitter. Both the dead time and the data-dependent timing jitter are major limiting factors in designing QKD systems with sifted-key rates beyond Mbit/s.
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.
We have implemented a quantum key distribution (QKD) system with polarization encoding at 850 nm over 1 km of optical fiber. The high-speed management of the bit-stream, generation of random numbers and processing of the sifting algorithm are all handled by a pair of custom data handling circuit boards. As a complete system using a clock rate of 1.25 Gbit/s, it produces sifted keys at a rate of 1.1 Mb/s with an error rate lower than 1.3% while operating at a transmission rate of 312.5 Mbit/s and a mean photon number μ = 0.1. With a number of proposed improvements this system has a potential for a higher key rate without an elevated error rate.
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.
A complete fiber-based polarization encoding quantum key distribution (QKD) system based on the BB84 protocol has been developed at National Institute of Standard and Technology (NIST). The system can be operated at a sifted key rate of more than 4 Mbit/s over optical fiber of length 1 km and mean photon number 0.1. The quantum channel uses 850 nm photons from attenuated high speed VCSELs and the classical channel uses 1550 nm light from normal commercial coarse wavelength division multiplexing devices. Sifted-key rates and quantum error rates at different transmission rates are measured as a function of distance (fiber length). A polarization auto-compensation module has been developed and utilized to recover the polarization state and to compensate for temporal drift. An automatic timing alignment device has also been developed to quickly handle the initial configuration of quantum channels so that detection events fall into the correct timing window. These automated functions make the system more practical for integration into existing optical local area networks.
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.