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arXiv:2207.07518 · Journal of the Optical Society of America B

Hybrid near-optimum binary receiver with realistic photon-number-resolving detectors

Michele N. Notarnicola, Matteo G. A. Paris, Stefano Olivares

Published Jan 18, 2023• 19 citations
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Abstract

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.

DOI
10.1364/josab.470806

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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.
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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 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.
We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using nonprobabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver is experimentally demonstrated and compared to an experimental realization of a homodyne receiver with postselection. In the comparison, it becomes clear that the performance of the PNR receiver surpasses the performance of the homodyne receiver, which we prove to be optimal within any Gaussian operations and conditional dynamics.
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.