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Acta Physica Sinica

The effect of balanced homodyne detection on continuous variable quantum key distribution

Jin-jian Chen, Zheng-Fu Han, Zhao Yi-Bo, Gui Youzhen, Guo Guang-Can, 中国科学技术大学，中科院量子信息重点实验室，合肥 230026

Published Jan 1, 2007• 4 citations
Publisher

Abstract

Different from single photon quantum key distribution, continuous variable quantum key distribution uses the balanced homodyne detection. In this paper, the detection error of balanced homodyne caused by vacuum noise of the local light and unbalance of beam splitter is analyzed, the maximal safe distance limited by the electronic noise of balance homodyne detector is given, finally, the relationship between the noise of balanced homodyne detection and key rate are shown.

DOI
10.7498/aps.56.5

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Different from single photon quantum key distribution, continuous variable quantum key distribution uses the balanced homodyne detection. In this paper, the detection error of balanced homodyne caused by vacuum noise of the local light and unbalance of beam splitter is analyzed, the maximal safe distance limited by the electronic noise of balance homodyne detector is given, finally, the relationship between the noise of balanced homodyne detection and key rate are shown.
Abstract The time-domain balanced homodyne detector (TBHD) is critical component in continuous-variable quantum key distribution (CVQKD). The shot-noise-limited attribute of a TBHD depends on the whole spectrum of detector, in contrast to a frequency-domain balanced homodyne detector that focuses only on part of the spectrum. We propose a method for accurate calibration of the shot-noise-limited attribute of the TBHD by overlapping the gain lines of the TBHD and an integrated photodetector. The overlapping of two lines indicates that the detector is indeed shot noise limited, which is crucial to the security of CVQKD. Experimentally, we use this method to obtain a calibration error of ±1‰. Theoretical analysis showed that the CVQKD performance is very sensitive to calibration errors of shot noise, and proper countermeasures should be employed to eliminate this issue. The presented methods are expected to contribute to CVQKD security and TBHD standardization.
In Gaussian-modulated coherent-state quantum key distribution, the measurement of quadratures of coherent states is performed by using a homodyne detector. However, conventional detectors usually suffer from narrow bands. We present a method to design a high-speed shot-noise-limited balanced homodyne detector. A 300-MHz bandwidth detector is experimentally tested and the level of shot noise is 14 dB higher than the electronic noise. The results show that a detector with this method is potential to design a GHz bandwidth detector for continuous variable quantum key distribution at a low level of ratio of shot noise to electronic noise.
In continuous-variable quantum key distribution (CV-QKD), the key information are encoded on quadratures of the optical field, which are measured via balanced homodyne detector (BHD). The bandwidth of the BHD is one of key parameters for precise characterization of quantum states. We establish a theoretical model to analyze the impact of the BHD bandwidth and signal modulation patterns on the channel parameters estimation of CV-QKD systems. Based on the proposed model, the secure key rate of a practical CV-QKD system under different BHD bandwidths and signal modulation patterns are investigated. Our results show that insufficient BHD bandwidth will result in wrong estimate of the transmission loss and excess noise, which significantly affects the performance of CV-QKD systems. Given the BHD bandwidth, there exists an optimal signal repetition rate that maximizes the secure key rate. The BHD bandwidth requirement of the QKD system increases with the transmission distance for large duty cycle pulse. Furthermore, the root raised-cosine pulse signal modulation performs better than the square pulse signal modulation in general.
We propose a rigorous calibration method for homodyne detection efficiency, which combines all the factors that affect detection efficiency to calibrate together through the actual homodyne detection. With this method, the transmittance converted from electronic noise in the one-time calibration method of the shot noise can be attributed to the detection inefficiency. Thus, a trusted detection noise-free model for continuous-variable quantum key distribution (CV-QKD) can be established, which simplifies the calibration of shot noise while having the same performance as the trusted detection noise model. We demonstrate this calibration method with a balanced detector based on a transimpedance amplifier. Experimental results show that detection efficiency will be overestimated if the integration factor of the detector is overlooked. The overestimation of the detection efficiency leads to an underestimation of modulation variance and excess noise when the modulation variance is monitored by the balanced detector, which opens security loopholes. Our method may prove a necessary method in the calibration of detection efficiency for CV-QKD.
We evaluate the performance of Gaussian Modulated Coherent State (GMCS) Continuous-Variable Quantum Key Distribution (CV-QKD), in terms of secure key rate, at different detector bandwidths. We illustrate the advantages and limitations of high-speed CV-QKD systems using a general noise model in which we consider various noise sources and their dependence upon detection bandwidth. Experimentally, the feasibility of high speed CV-QKD is demonstrated by using a GHz bandwidth balanced homodyne detector (BHD) established with commercially available components. We provide secure key rates of transmitted and local local oscillator schemes under various clock rates.
Quantum key distribution (QKD) systems based on the modulation of weak-coherent states and homodyne detection has attracted much attention over last years due to its compatibility with existing telecom equipment. The coherent state required by most of the practical protocols for continuous-variable QKD can be produced in practice using a typical laser source followed by standard phase and amplitude optical modulators. On the other hand, the homodyne detector used to measure the quadratures of the modulated light field can be implemented with high-efficient PIN photodiodes. Moreover, in continuous-variable QKD systems the security of the secret key depends on the precise estimation by Bob of the loss and excess noise of the quantum channel. In this work we discuss the impact of imperfect state preparation by Alice and the role of homodyne detector imbalance on the performance of a continuous-variable QKD system. More specifically, we will consider that Alice phase and amplitude modulators are not ideal suffering from incorrect modulation calibration and optical imbalance, and that the positive and negative currents of Bob homodyne detector are not completely canceled due to a non-ideal beam-splitter and due to different quantum efficiencies of its two photodiodes.