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Optics Express

Heterodyne-like feedforward partitioned-displacement hybrid receiver for QPSK coherent state discrimination with realistic photon-number-resolving detectors

enhao bai, Tianyi Wu, Fengkai Sun, Jian Jun Peng, Zichao Zhou, Chen Dong, Zhang Zhenrong

Published Dec 9, 2025• 2 citations
Publisher

Abstract

This paper proposes a hybrid receiver, the heterodyne-like feedforward partitioned-displacement hybrid (HFPH) receiver, for discriminating quadrature phase-shift keying (QPSK) coherent states using photon-number-resolving (PNR) detectors. The receiver integrates a heterodyne-like (HL) measurement scheme with a Shuro-like (SL) displacement backend, forming a feedforward architecture that dynamically adapts to real-time decisions. We theoretically analyze the performance of the proposed scheme under practical imperfections, including detection inefficiency, dark counts, and imperfect interference visibility. Our results demonstrate that the HFPH receiver can surpass the standard quantum limit under these non-ideal conditions and exhibits enhanced robustness compared to the benchmark receiver.

DOI
10.1364/oe.576111

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This paper proposes a hybrid receiver, the heterodyne-like feedforward partitioned-displacement hybrid (HFPH) receiver, for discriminating quadrature phase-shift keying (QPSK) coherent states using photon-number-resolving (PNR) detectors. The receiver integrates a heterodyne-like (HL) measurement scheme with a Shuro-like (SL) displacement backend, forming a feedforward architecture that dynamically adapts to real-time decisions. We theoretically analyze the performance of the proposed scheme under practical imperfections, including detection inefficiency, dark counts, and imperfect interference visibility. Our results demonstrate that the HFPH receiver can surpass the standard quantum limit under these non-ideal conditions and exhibits enhanced robustness compared to the benchmark receiver.
We propose a hybrid feed-forward receiver (HFFRE) for the discrimination of binary phase-shift-keyed coherent states based on the appropriate combination of a displacement feed-forward receiver (DFFRE) and a homodynelike setup employing a low-intensity local oscillator and photon-number-resolving detectors. We investigate the performance of the proposed scheme, also addressing realistic scenarios in the presence of nonunit quantum detection efficiency, dark counts, and visibility reduction. The present HFFRE outperforms the DFFRE in all conditions, beating the standard quantum limit in particular regimes.
We propose a near-optimum receiver for the discrimination of binary phase-shift-keyed coherent states employing photon-number-resolving detectors. The receiver exploits a discrimination strategy based on both so-called homodyne-like and direct detection, thus resulting in a hybrid scheme. We analyze the performance and robustness of the proposed scheme under realistic conditions, namely, in the presence of inefficient detection and dark counts. We show that the present hybrid setup is near- optimum and beats both the standard quantum limit and the performance of the Kennedy receiver.
We propose and experimentally demonstrate a near-optimal discrimination scheme for the quadrature phase shift keying (QPSK) protocol. We show in theory that the performance of our hybrid scheme is superior to the standard scheme—heterodyne detection—for all signal amplitudes and underpin the predictions with our experimental results. Furthermore, our scheme provides hitherto the best performance in the domain of highly attenuated signals. The discrimination is composed of a quadrature measurement, a conditional displacement and a threshold detector.
This paper proposes a multichannel optimal squeezing-displacement receiver (MOSDR) with photon-number-resolving detectors for discriminating binary phase-shift keying (BPSK) coherent states. Unlike previous squeezing-based receivers whose gain is largely limited to the low photon-number regime, we partition the input signal into multiple channels so that the mean photon number in each channel is reduced, allowing the squeezing operation to be used more effectively in its favorable operating region. In addition, we use displacement feedforward between channels and accumulate the per-channel discrimination outcomes through a sequential decision process, thereby reducing the overall error probability. We analyze MOSDR under an ideal detector as well as under quantum efficiency, dark counts and visibility reduction. The results show that MOSDR outperforms an optimized-displacement multichannel displacement feedforward receiver and remains below the standard quantum limit over a wide photon-number range, exhibiting improved robustness to detection imperfections.
The quantum receiver is an important tool for overcoming the standard quantum limit (SQL) of discrimination errors in optical communication. We theoretically study the quantum receivers for discriminating ternary and quaternary phase-shift-keying coherent states in terms of average error rate and mutual information. Our receiver consists of on-off--type photon detectors and displacement operations without electrical feedforward operations. We show that for the ternary signals, the receiver shows a reasonable gain from the SQL even without feedforward. This scheme is realizable with the currently available technology. For the quaternary signals feedforward operation is crucial to overcome the SQL with imperfect devices. We also analytically examine the asymptotic limit of the performance of the proposed receiver with respect to the number of feedforward steps.
We propose quantum receivers with optical squeezing and photon-number-resolving detectors (PNRDs) for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals. The basic scheme is similar to the previous proposals [e.g., Izumi et al., Phys. Rev. A 86, 042328 (2012)] in which displacement operations, on-off detectors, and electrical feedforward operations were used. Here we study two types of receivers, one of which installs optical squeezings and the other uses PNRDs instead of on-off detectors. We show that both receivers can attain lower error rates than that in the previous scheme. In particular, we show the PNRD-based receiver has a significant gain when the ratio between the mean photon number of the signal and the number of the feedforward steps is relatively high, in other words, when the probability of detecting two or more photons at each detector is not negligible. Moreover, we show that the PNRD-based receiver can suppress the errors due to dark counts, which the receiver with the on-off detector cannot do with a small number of feedforwards.