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IEEE Communications Letters

Kennedy Receiver Using Threshold Detection and Optimized Displacement Under Thermal Noise

Renzhi Yuan, Mufei Zhao, Shuai Han, Julian Cheng

Published Mar 13, 2020• 29 citations
Publisher

Abstract

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.

DOI
10.1109/lcomm.2020.2980537

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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.
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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.
We propose an inverse-squeezing Kennedy receiver for discriminating binary phase-shift-keyed displaced squeezed vacuum states. The receiver combines a Kennedy-type nulling displacement, an orthogonally oriented inverse-squeezing operation and photon-number-resolving detection with a maximum-a-\emph{posteriori} threshold rule. Its key mechanism is that the inverse-squeezing stage converts transmitter-side squeezing into enhanced photon-number contrast, or equivalently an effective coherent-state energy gain, that can be directly exploited at the measurement stage. Under ideal equal-prior conditions, the receiver surpasses the standard quantum limit for squeezed-state binary phase-shift keying at approximately N≈0.3N\approx 0.3N≈0.3, outperforms the Helstrom bound of coherent-state binary phase-shift keying at approximately N≈0.4N\approx 0.4N≈0.4, and reaches the 1\% error level near N≈0.6N\approx 0.6N≈0.6. We further analyze its performance under realistic imperfections, including finite detector efficiency, dark counts, channel phase diffusion, receiver thermal noise and transmission loss. The results show that adaptive thresholding preserves robust performance against detector and noise imperfections over practical parameter ranges, whereas transmission loss progressively suppresses the squeezing-enabled advantage. These findings indicate that, for the fixed source parametrization adopted in this work, the proposed receiver is most advantageous in the low-loss regime, especially at low source energies.
An optical quantum communication system with receiver diversity is proposed for free-space communication using the optical combining technique and a generalized Kennedy receiver. The quantum channel model of the proposed system is established using the P -representation in the presence of both turbulence and thermal noise. A conditional dynamics based Kennedy receiver with threshold detection is proposed to mitigate the influence of both turbulence and thermal noise. The error probabilities for different types of generalized Kennedy receiver, i.e., the Kennedy receiver, the Type-II receiver, and the conditional dynamics based Kennedy receiver, are analytically studied and the lower bounds for these error probabilities are obtained. Numerical results show that both the Kennedy receiver and the Type-II receiver fail in the presence of either turbulence or thermal noise. The performance of the proposed conditional dynamics based Kennedy receiver with threshold detection can surpass the standard quantum limit given by the homodyne receiver in either weak turbulence or small thermal noise.
Displacement based quantum receivers can beat the standard quantum limit and have gained increasing attention in recent years. The displacement operation value can be estimated and calibrated by using Fock states as probes. In this Letter, we focus on the impacts of thermal noise when preparing the Fock probes on the estimation performance. We first derive the density matrix and the photon statistics of the noisy displaced number state with a uniformly distributed displacement phase. Based on the derived density matrix, we then analyze the performance of estimating displacement operations by using the maximum likelihood estimation (MLE) method. To decrease the computational complexity of the MLE, we further derive an approximated probability density of the photon numbers under small displacement. Besides, the quantum Cramér–Rao bound (QCRB) is also derived to analyze the performance limit of the displacement estimation. Numerical results found that, though thermal noise can greatly degrade the MLE accuracy of the displacement operations, the performance advantage of using Fock probes still persists over classical coherent probes. Besides, we demonstrate that the MLE method based on Fock probes can well approach the QCRB when the displacement strength N c ≤ ~1.
Displacement based quantum receivers have gained increasing attention because they can beat the standard quantum limit. The displacement value in quantum receivers can be calibrated by using number states as probes. Current estimating methods assumed that ideal number states can be prepared perfectly, which is impossible in practical implementations. In this work, we focus on the impacts of thermal noise when preparing the number states on the estimation performance of displacement operations. We first derive the probability density of photon numbers in a thermal noise contaminated number state after a displacement operation, which we call the noisy displaced number state (NDNS). Based on the derived probability density, we then analyze the performance of estimating displacement operations with NDNS probes by using the maximum likelihood estimation (MLE) method. Numerical results found that the thermal noise in preparing the number states has great influence on the MLE accuracy of the displacement operations.