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IEEE Transactions on Communications

Phase and Intensity Noise Tracking for Time-Resolving Quantum Receivers

Yufei Suo, Bing Zhu

Published Jan 27, 2025• 2 citations
Publisher

Abstract

Employing quantum receivers to discriminate laser coherent states makes it feasible to achieve error probabilities below the standard quantum limit (SQL), particularly for photon-starved optical communication. However, the quantum receiver performance for phase shift keyed coherent states is severely degraded by random phase and intensity noise in realistic communication channels. This paper proposes a phase and intensity noise-tracking method based on the cubature Kalman filter (CKF) to improve the performance of time-resolving quantum receivers. The filter leverages the data collected during time-resolving state discrimination to perform real-time estimation and correction of time-varying phase and intensity noise. By conducting numerical simulations, we demonstrate that the proposed noise-tracking method enables the time-resolving quantum receiver to retain its superiority over the SQL while requiring significantly less computational effort than a Bayesian estimator. Additionally, the robustness against practical imperfections, including dead time and dark count rate of single photon detector (SPD), is shown through the simulations.

DOI
10.1109/tcomm.2025.3534525

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Employing quantum receivers to discriminate laser coherent states makes it feasible to achieve error probabilities below the standard quantum limit (SQL), particularly for photon-starved optical communication. However, the quantum receiver performance for phase shift keyed coherent states is severely degraded by random phase and intensity noise in realistic communication channels. This paper proposes a phase and intensity noise-tracking method based on the cubature Kalman filter (CKF) to improve the performance of time-resolving quantum receivers. The filter leverages the data collected during time-resolving state discrimination to perform real-time estimation and correction of time-varying phase and intensity noise. By conducting numerical simulations, we demonstrate that the proposed noise-tracking method enables the time-resolving quantum receiver to retain its superiority over the SQL while requiring significantly less computational effort than a Bayesian estimator. Additionally, the robustness against practical imperfections, including dead time and dark count rate of single photon detector (SPD), is shown through the simulations.
Non-conventional receivers for phase-coherent states based on non-Gaussian measurements such as photon counting surpass the sensitivity limits of shot-noise-limited coherent receivers, the quantum noise limit (QNL). These non-Gaussian receivers can have a significant impact in future coherent communication technologies. However, random phase changes in realistic communication channels, such as optical fibers, present serious challenges for extracting the information encoded in coherent states. While there are methods for correcting random phase noise with conventional heterodyne detection, phase-tracking for non-Gaussian receivers surpassing the QNL is still an open problem. Here we demonstrate phase tracking for non-Gaussian receivers to correct for time-varying phase noise while allowing for decoding beyond the QNL. The phase-tracking method performs real-time parameter estimation and correction of phase drifts using the data from the non-Gaussian discrimination measurement, without relying on phase reference pilot fields. This method enables non-Gaussian receivers to achieve higher sensitivities and rates of information transfer than ideal coherent receivers in realistic channels with time-varying phase noise. This demonstration makes sub-QNL receivers a more robust, feasible, and practical quantum technology for classical and quantum communications.
Non-Gaussian receivers for optical communication with coherent states can achieve measurement sensitivities beyond the limits of conventional detection, given by the quantum-noise limit (QNL).However, the amount of information that can be reliably transmitted substantially degrades if there is noise in the communication channel, unless the receiver is able to efficiently compensate for such noise.Here, we investigate the use of a deep neural network as a computationally efficient estimator of phase and amplitude channel noise to enable a reliable method for noise tracking for non-Gaussian receivers.The neural network uses the data collected by the non-Gaussian receiver to estimate and correct for dynamic channel noise in real time.Using numerical simulations, we find that this noise tracking method allows the non-Gaussian receiver to maintain its benefit over the QNL across a broad range of strengths and bandwidths of phase and intensity noise.The noise tracking method based on neural networks can further include other types of noise to ensure sub-QNL performance in channels with many sources of noise.
Phase estimation represents a crucial challenge in many fields of Physics, ranging from Quantum Metrology to Quantum Information Processing. This task is usually pursued by means of interferometric schemes, in which the choice of the input states and of the detection apparatus is aimed at minimizing the uncertainty in the estimation of the relative phase between the inputs. State discrimination protocols in communication channels with coherent states also require the monitoring of the optical phase. Therefore, the problem of phase estimation is relevant to face the issue of coherent states discrimination. Here we consider a quasi-optimal Kennedy-like receiver, based on the interference of two coherent signals, to be discriminated, with a reference local oscillator. By means of the Bayesian processing of a small amount of data drawn from the outputs of the shot-by-shot discrimination protocol, we demonstrate the achievement of the minimum uncertainty in phase estimation, also in the presence of uniform phase noise. Moreover, we show that the use of photon-number resolving detectors in the receiver improves the phase-estimation strategy, especially with respect to the usually employed on/off detectors. From the experimental point of view, this comparison is realized by employing hybrid photodetectors.
The Kennedy-like receiver is a quasi-optimal discrimination scheme employed in binary phase-shift-keyed communication schemes with coherent states. In its standard configuration, it is based on the interference of the two signals encoding the message with a reference local oscillator and on the measurement by means of ON/OFF detectors. Here we demonstrate that, without interrupting the communication, it is possible to monitor the relative phase between the signals and the local oscillator by applying a Bayesian processing to the very data sample used to discriminate the signals at any shot. We show, both numerically and experimentally, that the minimum uncertainty in phase estimation can be achieved both with ON/OFF and photon-number resolving detectors. The performances of our phase-estimation method in the presence of either uniform phase noise or phase diffusion are also investigated and discussed.
The impossibility of perfectly discriminating non-orthogonal quantum states imposes far-reaching consequences both on quantum and classical communication schemes.Wepropose and numerically analyze an optimized quantum receiver for the discrimination of phase encoded signals. Our scheme outperforms the standard quantum limit and approaches the Helstrom bound for any signal power. The discrimination is performed via an optimized, feedback-mediated displacement prior to a photon counting detector.Weprovide a detailed analysis of the influence of excess noise and technical imperfections on the average error probability. The results demonstrate the receiver’s robustness and show that it can outperform any classical receiver over a wide range of realistic parameters.
The continuous-variable quantum key distribution with a local local-oscillator is extremely sensitive to the phase compensation noise caused by the inaccurate reference phase estimation. In order to overcome the influence of slow drift caused by the residual optical frequency difference, we utilize a vector Kalman filter to estimate and track the reference phase from pilots. The fast drift and slow drift are taken into account in the variation of the reference phase, so that phase estimation becomes more accurate than the conventional scalar Kalman filter. The mean square error of reference phase estimation is deduced theoretically, and the specified frame is designed to estimate the phase noise variance in real time. In simulations, the performances involving of the estimation accuracy, the actual excess noise and the secret key rate are compared between with four different phase estimation methods. The simulation results show that the vector Kalman filter is superior to the other methods, even though under a serious phase noise and a large optical frequency difference.