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Scientific Reports

Phase-reference monitoring in coherent-state discrimination assisted by a photon-number resolving detector

Matteo Bina, Alessia Allevi, Maria Bondani, Stefano Olivares

Published May 18, 2016• 25 citations
Publisher

Abstract

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.

DOI
10.1038/srep26025

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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 Kennedy-like receiver is a quasi-optimal receiver employed in binary phase-shift-keyed communication schemes with coherent states. It is based on the interference of the two signals encoding the message with a reference local oscillator and on/off photodetection. We show both theoretically and experimentally that it is possible to extract useful information about the phase reference by Bayesian processing of the very same data sample used to discriminate the signals shot by shot. We demonstrate that the minimum uncertainty in phase estimation, given by the inverse of the Fisher information associated with the statistics of the collected data, can be achieved. We also numerically and experimentally investigate the performances of our phase-estimation method in the presence of phase noise, when either on/off or photon-number resolving detectors are employed.
We propose a homodyne-like detection scheme involving photon-number-resolving detectors to discriminate between two coherent states affected by either uniform or gaussian phase noise. A proof-of-principle experiment is performed employing two hybrid photodetectors, whose outputs are used in post processing to calculate the shot-by-shot photon-number differences. The performance of the strategy is quantified in terms of the error probability in discriminating the noisy coherent signals as a function of the characteristic noise parameters.
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.
Over the past decade, binary phase-shift-keying encoding has been used as a benchmark to test the performance of different detection strategies to address the problem of state discrimination. In this context, hybrid devices, giving access to both particle- and wave-like properties of light, could offer the possibility to better discriminate the sent signals. In this work, we consider a quantum channel exploiting a hybrid receiver embedding Silicon photomultipliers as photon-number-resolving detectors. We retrieve the discrimination error probability and the mutual information between sender and receiver as functions of some relevant experimental parameters in the case of binary phase-shifted coherent states. Our promising results, supported also with numerical simulations and theoretical analysis, foster further using this kind of hybrid receiver in more complex detection schemes. • We address state discrimination by a Silicon photomultiplier-based hybrid receiver. • The hybrid receiver gives access to particle- and wave-like properties of light. • We consider error probability and mutual information in a BPSK scenario.
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.