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International Wireless Communications and Mobile Computing Conference (IWCMC)

Post-selection Based Generalized Kennedy Receiver for Discriminating Binary Coherent States

Mufei Zhao, Renzhi Yuan, Julian Cheng, Shuai Han

Published Jun 28, 2021• 3 citations
Publisher

Abstract

The generalized Kennedy receiver can be used to improve the secret key rate of continuous variable quantum key distribution protocol and thus attracts much attention recently. In this letter, we analytically study the performance of the post-selection based generalized Kennedy receiver in the presence of thermal noise. To improve the performance of the generalized Kennedy receiver, we optimize the displacement operation for different post-selection parameter and different thermal noises. Numerical results show that the thermal noise can greatly degrade the performance of the post-selection based generalized Kennedy receiver. Besides, the resistance of the generalized Kennedy receiver to the thermal noise can be improved by choosing an appropriate post-selection parameter.

DOI
10.1109/iwcmc51323.2021.9498804

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The generalized Kennedy receiver can be used to improve the secret key rate of continuous variable quantum key distribution protocol and thus attracts much attention recently. In this letter, we analytically study the performance of the post-selection based generalized Kennedy receiver in the presence of thermal noise. To improve the performance of the generalized Kennedy receiver, we optimize the displacement operation for different post-selection parameter and different thermal noises. Numerical results show that the thermal noise can greatly degrade the performance of the post-selection based generalized Kennedy receiver. Besides, the resistance of the generalized Kennedy receiver to the thermal noise can be improved by choosing an appropriate post-selection parameter.
Continuous variable quantum key distribution attracts increasing attention in recent years due to its potential high secret key rates and the compatibility with existing communication infrastructure. This letter derives the secret key rate for a binary modulated continuous variable quantum key distribution using an optimally displaced threshold detection and post-selection. To improve the secret key rate, we optimize the post selected area and the coherent amplitude for different transmission efficiency of the channel under different thermal noises. Both the individual and collective beamsplitter attacks are considered. Numerical results show that the secret key rate using the optimally displaced threshold detection can surpass that using the classical detection scheme under different transmission efficiencies and different thermal noises. Besides, more improvement on the secret key rate can be obtained when the transmission efficiency is low.
The performance of Kennedy receiver with threshold detection is analyzed in the presence of thermal noise. A lower bound is first derived for the error probability of the Kennedy receiver in the presence of thermal noise and it is shown that the performance of the Kennedy receiver is greatly affected by the thermal noise. Then we analyze the performance of the Kennedy receiver using the maximum a posteriori detection, which is proven to be equivalent to a threshold detection. We also optimize the displacement operation to improve further the receiver performance. Numerical results show that the Kennedy receiver with threshold detection can surpass the standard quantum limit achieved by homodyne detection when the average number of thermal photons is smaller than 0.1. The Kennedy receiver with threshold detection using optimized displacement can surpass the standard quantum limit when the average number of thermal photons is smaller than 0.2.
Near-optimal binary coherent state discrimination can be achieved by performing a displacement operation followed by photon detection. This displacement serves as a control parameter that can be tuned to optimize a chosen figure of merit, which makes such receivers attractive beyond state discrimination. Here, we turn this discrimination strategy into a complete continuous-variable quantum key distribution (CV-QKD) protocol based on a binary alphabet of noisy coherent states (displaced thermal states) and displacement receivers. We develop a strategy for estimating the channel parameters with the same displacement receiver, since standard quadrature-based methods do not apply. While a key map can be obtained with on/off detection, we demonstrate that reliable parameter estimation requires photon-number-resolving detection with sufficient resolution. Finite detector resolution underestimates the observed noise and constitutes a potential security loophole, which we quantify and show to be mitigable with modest resolution. We analyze the protocol's security against entangling-cloner collective attacks in the asymptotic regime, for both direct and reverse reconciliation, and show that it can generate secret keys even under noisy state preparation and imperfect detection. Interestingly, we find that the displacement that minimizes the discrimination error probability also performs well for key generation, thus providing a useful and analytically tractable tuning strategy for the CV-QKD receiver. We evaluate the protocol's performance over a range of transmittances and noise parameters, showing that the displacement receiver can outperform conventional homodyne detection in experimentally relevant regimes. Together, our results point to displacement receivers as a promising alternative for CV-QKD implementations.
Endogenous security in next-generation wireless communication systems attracts increasing attentions in recent years. A typical solution to endogenous security problems is the Quantum Key Distribution (QKD), where unconditional security can be achieved thanks to the inherent properties of quantum mechanics. Continuous Variable-Quantum Key Distribution (CV-QKD) enjoys high Secret Key Rate (SKR) and good compatibility with existing optical communication infrastructure. Traditional CV-QKD usually employ coherent receivers to detect coherent states, whose detection performance is restricted to the standard quantum limit. In this paper, we employ a generalized Kennedy receiver called CD-Kennedy receiver to enhance the detection performance of coherent states in turbulent channels, where Equal-Gain Combining (EGC) method is used to combine the output of CD-Kennedy receivers. Besides, we derive the SKR of a post-selection based CV-QKD protocol using both CD-Kennedy receiver and homodyne receiver with EGC in turbulent channels. We further propose an equivalent transmittance method to facilitate the calculation of both the Bit-Error Rate (BER) and SKR. Numerical results show that the CD-Kennedy receiver can outperform the homodyne receiver in turbulent channels in terms of both BER and SKR performance. We find that BER and SKR performance advantage of CD-Kennedy receiver over homodyne receiver demonstrate opposite trends as the average transmittance increases, which indicates that two separate system settings should be employed for communication and key distribution purposes. Besides, we also demonstrate that the SKR performance of a CD-Kennedy receiver is much robust than that of a homodyne receiver in turbulent channels.
Security analysis of continuous variable quantum key distribution (CV-QKD) remains a topic of extensive academic investigation. In this work, we propose a coherent-state CV-QKD protocol integrating a displacement-based quantum receiver and post-selection strategies. We establish a framework of the protocol under both individual and collective attacks, incorporating practical constraints such as noises and device imperfections. To enhance performance of the protocol, the postselection strategy and the transmitted signal power are optimized for different channel attenuation levels. Numerical results offer insights into the strategy of employing displacement receivers in CV-QKD protocols, revealing that larger transmitted signal power is required under low channel attenuation or severe receiver-side imperfections and noises to achieve higher the secret key rate.
Continuous variable quantum key distribution (CV-QKD) protocol has drawn much attention due to its compatibility with existing optical communication systems. In this paper, we propose a quaternary modulated CV-QKD protocol using displacement receivers and adopt the post-selection scheme to overcome the ‘3dB limit’. We first establish the model of displacement receiver for discriminating quaternary modulated coherent signals in a realistic situation. The performance of non-adaptive displacement receiver and multi-stage feedforward receiver are both investigated under different noises and device imperfections. To improve the receiver performance, we numerically optimize the displacement operation and check the quantum advantage of the displacement receivers over the classical homodyne detection. Then we analyze the security of the proposed CV-QKD protocol. The secret key rate is derived for both types of displacement receivers under the collective beam splitting attack. We also optimize the transmitted signal photons for different channel transmission efficiencies under practical system constraints. Numerical results shed light on the practical application of displacement receivers in CV-QKD protocols. This includes evaluating the necessity of optimizing the displacement and incorporating the feedforward structure in a displacement receiver according to different practical system limitations. Moreover, under higher channel transmission efficiency and increased receiver noise level, a larger coherent amplitude is required for transmitting signals to attain the maximum secret key rate.