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.
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.
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.
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.
The quantum communication process usually consists of three stages: the sender who prepares encoded carriers, the transmission in noisy channels, and the quantum receivers. The transmitted quantum information can be inevitably affected by kinds of quantum noise in the environment. Thus, quantum protocols are extensively studied to improve communication efficiency and accuracy under the influence of quantum noise. The optimization strategies usually occur in these three stages. In this paper, we focus on the optimization strategy of quantum receivers in the third stage. In quantum receiver algorithms, the key to distinguish received non-orthogonal coherent states in free-space optical quantum communication is to construct an optimum displacement operator for transforming the current coherent state into a state that is easier to distinguish than before. To improve the antinoise ability and accuracy of quantum communication, this paper proposes a universal optimization strategy of quantum receivers called learnable antinoise receiver (LAN receiver). In this strategy, a parametrized quantum circuit is constructed as a quantum feedforward neural network as the displacement operator to improve the antinoise ability. The parameters used in the quantum circuit are updated by gradient descent continuously to find the best parameter combination of the quantum circuit that minimizes the error rate and the qubits affected by quantum noise are used as training and testing data. The simulation of the proposed algorithm shows that the LAN receiver can resist different kinds of strong quantum noise. The average error rate of the proposed algorithm LAN receiver under the strong noise channel is 0.18, which has better performance than other type of receivers under the influence of strong quantum noise.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated codewords with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations (passive linear optics: beamsplitters and phase-shifters, second order nonlinear process (squeezers), along with homodyne or heterodyne detection measurements) and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communications, one has to incorporate non-Gaussian (i.e. higher order nonlinear) operations in the receiver.
Laser-light (coherent-state) modulation is sufficient to achieve the ultimate (Holevo) capacity of classical communication over a lossy and noisy optical channel, but requires a receiver that jointly detects long modulated code words with highly nonlinear quantum operations, which are near-impossible to realize using current technology. We analyze the capacity of the lossy-noisy optical channel when the transmitter uses coherent-state modulation but the receiver is restricted to a general quantum-limited Gaussian receiver, i.e., one that may involve arbitrary combinations of Gaussian operations [passive linear optics: beam splitters and phase shifters; second-order nonlinear optics (or active linear optics): squeezers, along with homodyne or heterodyne detection measurements] and any amount of classical feedforward within the receiver. Under these assumptions, we show that the Gaussian receiver that attains the maximum mutual information is either homodyne detection, heterodyne detection, or time sharing between the two, depending upon the received power level. In other words, our result shows that to exceed the theoretical limit of conventional coherent optical communication, one has to incorporate non-Gaussian, i.e., third- or higher-order nonlinear operations in the receiver. Finally we compare our Gaussian receiver limit with experimentally feasible non-Gaussian receivers and show that in the regime of low received photon flux, it is possible to overcome the Gaussian receiver limit by relatively simple non-Gaussian receivers based on photon counting.
Coherent measurement of quantum signals used for continuous-variable (CV) quantum key distribution (QKD) across satellite-to-ground channels requires compensation of phase wavefront distortions caused by atmospheric turbulence. One compensation technique involves multiplexing classical reference pulses (RPs) and the quantum signal, with direct phase measurements on the RPs then used to modulate a real local oscillator (RLO) on the ground - a solution that also removes some known attacks on CV-QKD. However, this is a cumbersome task in practice - requiring substantial complexity in equipment requirements and deployment. As an alternative to this traditional practice, here we introduce a new method for estimating phase corrections for an RLO by using only intensity measurements from RPs as input to a convolutional neural network, mitigating completely the necessity to measure phase wavefronts directly. We show that the phase correction accuracy needed to provide for non-zero secure key rates through satellite-to-ground channels is achieved by our intensity-only measurements. Our work shows, for the first time, how artificial intelligence algorithms can replace phase-measuring equipment in the context of CV-QKD delivered from space, thereby delivering an alternate deployment paradigm for this global quantum-communication application.