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Acta Physica Sinica

The influence of the time delay through long trunk fiber on the phase-coding quantum key distribution system

Jindong Wang, Zhengjun Wei, Hui Zhang, Zhang Hua-Ni, Chen Shuai, Qin Xiao-Juan, Jianping Guo, Liao Chang-Jun, Songhao Liu

Published Jan 1, 2010• 2 citations
Publisher

Abstract

Optical pulse will reach the receiver not at exact time instance due to the transmission through the long trunk fiber, and this phenomenon will effect on the bits error rate in the Quantum key distribution (QKD) system to some extend. The time jitter based on the differential phase shift quantum key distribution system and two asymmetric Mach-Zehnder interferometers is measured outdoors in different transmission distance and the physical model of the relationship between the time jitter and the quantum bit error rate is proposed. According to this relationship, the quantum bit error rate can be estimated for some optical pulse shape and some statistical distribution function.

DOI
10.7498/aps.59.5514

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Optical pulse will reach the receiver not at exact time instance due to the transmission through the long trunk fiber, and this phenomenon will effect on the bits error rate in the Quantum key distribution (QKD) system to some extend. The time jitter based on the differential phase shift quantum key distribution system and two asymmetric Mach-Zehnder interferometers is measured outdoors in different transmission distance and the physical model of the relationship between the time jitter and the quantum bit error rate is proposed. According to this relationship, the quantum bit error rate can be estimated for some optical pulse shape and some statistical distribution function.
Quantum Key Distribution (QKD) system based on the two asymmetric Mach-Zehnder optical fiber interferometers is easily influenced by the external environmental interference, which causes phase excursion. And the high interference visibility of QKD system can’t keep for long and the instability of interference could cause the bit error of QKD. By tracking the stochastic phase excursion in statistical manner, the experiment of quantum key distribution over 75km was done successfully during the time of high interference visibility. The method of QKD in this paper is possessed of high security, less component, and easy operation.
Quantum bit error rate (QBER) of the quantum key distribution system based on the unbalanced Mach-Zehnder interferometer is theoretically analyzed. The influence of the unsymmetry of the two Mach-Zehnder interferometers, the birefringence in the fiber and the fluctuation of the temperature, on the QBER have been discussed in detail. The analytical expression of the QBER is deduced. It shows that the QBER caused by the unsymmetry of the two Mach-Zehnder interferometers defers to the Gauss distribution, QBER caused by the birefringence in the fiber which results in the disaccord of the polarization of the two pulses defers to the cosine distribution, and the fluctuation of the temperature exert great influence on the QBER.
Stability and robustness are important criteria to evaluate the performance of a quantum-key-distribution (QKD) system in real-life applications. However, the inherent birefringence effect of the fiber channel and disturbance caused by the variation of the deployment environment of the QKD system tremendously decrease its performance. To eliminate this adverse impact, we propose a polarization-insensitive phase-coding QKD system based on Sagnac--Mach-Zehnder interferometers. Verified by theoretical analysis and experimental tests, this QKD system is robust against channel polarization disturbance. The robustness and long-term stability of the QKD system is confirmed with a 10-day continuous operation over a 12.6-dB channel, which consists of a 50-km fiber spool and a polarization scrambler (2 rad/s). As a result, an average quantum bit error rate of 0.9580.958%0.958 and a sustained secure key rate of 3.68 kbps are obtained. Moreover, the secure key rate of the QKD system for a typical channel loss of 10 dB reaches 6.89 kbps, and the achievable maximum transmission distance exceeds 125 km.
Studied are the effects of fiber dispersion and loss and single-photon detector dark counts on key transmission rate and bit error rate of quantum key distribution system through theoretical analysis and computation. Research demonstrates that fiber loss is the main factor that influences quantum key transmission rate, while quantum bit error rate is related to fiber loss, dispersion, pulse width, dark counts and Rayleigh backscattering. Theoretical calculation indicates that in the current single-mode fiber-based plug & play quantum key distribution system with a dark counts of 10 -5/ns, the utilization of short pulse with 1550 nm wavelength and a 50 ps width can achieve the maximum transmission distance of 131 km. If we reduce dark counts or use G.653 dispersion-shifted fiber with short pulse, we can further improve key transmission rate and reduce the quantum bit error rate, thus effectively enhance the transmission distance of quantum key distribution system.
The hybrid modulation quantum key distribution(QKD) via single-photon two-qubit states scheme is analyzed,and an improvement scheme is proposed.The input-output model of polarization is established.And the influence of the interferometers on the polarization coding is analyzed.Quantum bit error rate(QBER) of polarization coding caused by the phasic error of fast and slow axes and the alignment error between the basis vectors of polarization and polarization axis is simulated.Furthermore,the stability conditions of polarization are derived on this basis.The QBER of polarization coding can be influenced deeply by the fiber M-Z interferometers.The theoretic analysis reveals that the jitter of polarization state is not only derived from the birefringency,but also derived from coordinate system difference between incident light and fast and slow axes in fiber interferometer.Some necessary conditoins for the QKD via single-photon two-qubit states are given.The simulation show that when ρ and θ are both below 0.2 rad,the polarization QBER is less than 0.015.When ρ and θ are both below 0.4 rad,the polarization QBER is less than 0.06.The polarization QBER of 2%-5% in two-qubit QKD scheme could be accepted as far as the safety upper limit of QBER(11%) is concerned.
Phase encoding in quantum key distribution (QKD) enables long-distance information-theoretic secure communication in optical fibers. We present a novel theoretical model characterizing errors from various sources in practical phase encoding-based QKD systems, namely the laser linewidth, detector dark counts, and channel dispersion. This model provides optimized optical pulse parameters and less distortion in pulses, which eliminates system imperfections and leads to a reduced quantum bit error rate (QBER) for practical QKD scenario. This analysis is applicable to various fiber-based phase and time encoding protocols. In particular, we implement this to a differential phase shift (DPS) QKD scheme operating at a 2.5 GHz clock, which produces a secure key rate of 193 bits/s at a fiber length of 265 km and an unprecedented QBER < 1[Formula: see text] up to 225 km length with standard telecom components. We show that by adjusting the quantum efficiency and dark count rates of detectors, proposed system can establish secure keys up to 380 km distance using standard telecom grade fiber with a QBER of 1.48%. Moreover, the system is compatible with existing optical fiber networks and capable of establishing a secure key exchange between two cities 432 km apart using ultra-low-loss (ULL) specialty fiber.