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arXiv:2308.02343 · Physical Review Applied

Imperfect photon detection in quantum illumination

Fabian Kronowetter, Michael Würth, Wolfgang Utschick, R. Gross, Kirill G. Fedorov

Published Jan 5, 2024• 10 citations
arXivHTMLPDF

Abstract

In quantum illumination, various detection schemes have been proposed for harnessing the remaining quantum correlations of the entanglement-based resource state. To date, the only successful implementation in the microwave domain [R. Assouly, R. Dassonneville, T. Peronnin, A. Bienfait, and B. Huard, Nat. Phys. 19, 1418 (2023)] has relied on a specific mixing operation of the respective return and idler modes, followed by single-photon counting in one of the two mixer outputs. We investigate the performance of this scheme for realistic detection parameters in terms of the detection efficiency, dark-count probability, and photon-number resolution. Furthermore, we take the second mixer output into account and investigate the advantage of correlated photon counting (CPC) for a varying thermal background and optimum postprocessing weighting in CPC. We find that the requirements for photon-number resolution in the two mixer outputs are highly asymmetric due to different associated photon-number expectation values.

DOI
10.1103/physrevapplied.21.014007

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In quantum illumination, various detection schemes have been proposed for harnessing the remaining quantum correlations of the entanglement-based resource state. To date, the only successful implementation in the microwave domain [R. Assouly, R. Dassonneville, T. Peronnin, A. Bienfait, and B. Huard, Nat. Phys. 19, 1418 (2023)] has relied on a specific mixing operation of the respective return and idler modes, followed by single-photon counting in one of the two mixer outputs. We investigate the performance of this scheme for realistic detection parameters in terms of the detection efficiency, dark-count probability, and photon-number resolution. Furthermore, we take the second mixer output into account and investigate the advantage of correlated photon counting (CPC) for a varying thermal background and optimum postprocessing weighting in CPC. We find that the requirements for photon-number resolution in the two mixer outputs are highly asymmetric due to different associated photon-number expectation values.
Entanglement is vulnerable to degradation in a noisy sensing scenario, but surprisingly, the quantum illumination protocol has demonstrated that its advantage can survive. However, designing a measurement system that realizes this advantage is challenging since the information is hidden in the weak correlation embedded in the noise at the receiver side. Recent progress in a correlation-to-displacement conversion module provides a route towards an optimal protocol for practical microwave quantum illumination. In this work, we extend the conversion module to accommodate experimental imperfections that are ubiquitous in microwave systems. To mitigate loss, we propose amplification of the return signals. In the case of ideal amplification, the entire six-decibel error-exponent advantage in target detection error can be maintained. However, in the case of noisy amplification, this advantage is reduced to three decibels. We analyze the quantum advantage under different scenarios with a Kennedy receiver in the final measurement. In the ideal case, the performance still achieves the optimal one over a fairly large range of error probability with only on-off detection. Empowered by photon-number-resolving detectors, the performance is further improved and also analyzed in terms of receiver operating characteristic curves. Our findings pave the way for the development of practical microwave quantum illumination systems.
Quantum illumination uses quantum correlations to improve the detection of objects in the presence of background noise. A simple and common practical approach to quantum illumination is to use threshold detectors to measure the idler mode. We investigate the optimization of these protocols. Surprisingly, we find that there can be an advantage to having a signal detector whose quantum efficiency is significantly less than perfect, one that does not vanish for low object reflectivities or signal strengths. We also show that decreasing the separation between pulses, while keeping the rate of photons transmitted per second fixed, can improve the performance, under appropriate conditions. We further show that postselecting on the idler detector firing is less efficient at object detection than not postselecting. Published by the American Physical Society 2024
Quantum illumination is a protocol where quantum resources are utilized to detect a low-reflectivity object embedded in a bright thermal noise bath. For example, quantum illumination with a two-mode squeezed state (TMSS) provides a 6 dB advantage in the error-probability exponent over the optimal classical illumination. We here consider quantum illumination with the photon-subtracted two-mode squeezed state (PSTMSS). Our result is twofold. First, we show that a much smaller error probability Perr{P}_{\mathrm{err}}Perr​ could be obtained, meaning that much smaller resources will be required in quantum illumination for a fixed Perr{P}_{\mathrm{err}}Perr​. Second, quantum illumination with PSTMSS appreciably outperforms its classic correspondence in both low- and high-noise operating regimes, extending the regimes in which quantum illumination is optimal for target detection.
It is important to find feasible measurement bounds for quantum information protocols. We present analytic bounds for quantum illumination with Gaussian states when using an on-off detection or a photon number resolving (PNR) detection, where its performance is evaluated with signal-to-noise ratio. First, for coincidence counting measurement, the best performance is given by the two-mode squeezed vacuum (TMSV) state which outperforms the coherent state and the classically correlated thermal (CCT) state. However, the coherent state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Second, the performance is enhanced by taking Fisher information approach with all counting probabilities including non-detection events. In the Fisher information approach, the TMSV state still presents the best performance but the CCT state can beat the TMSV state with increasing signal mean photon number in the case of the on-off detection. Furthermore, we show that it is useful to take the PNR detection on the signal mode and the on-off detection on the idler mode, which reaches similar performance of using PNR detection on both modes.
Single-photon detectors are an essential part of the toolbox of modern quantum optics for implementing quantum technologies and enabling tests of fundamental physics. The low energy of microwave photons, the natural signal path for superconducting quantum devices, makes their detection much harder than for visible light. Despite impressive progress in recent years and the proposal and realization of a number of different detector architectures, the reliable detection of a single itinerant microwave photon remains an open topic. Here, we investigate and simulate a detailed protocol for single-photon multiplication and subsequent amplification and detection. At its heart lies a Josephson-photonics device which uses inelastic Cooper-pair tunneling driven by a dc bias in combination with the energy of an incoming photon to create multiple photons, thus compensating for the low-energy problem. Our analysis provides clear design guidelines for utilizing such devices, which have previously been operated in an amplifier mode with a continuous wave input, for counting photons. Combining a formalism recently developed by Mølmer to describe the full quantum state of in- and outgoing photon pulses with stochastic Schrödinger equations, we can describe the full multiplication and detection protocol and calculate performance parameters, such as detection probabilities and dark count rates. With optimized parameters, a high population of a single output mode can be achieved that can then be easily distinguished from vacuum noise in heterodyne measurements of quadratures with a conventional linear amplifier. Realistic devices with two multiplication stages with multiplication of 161616 reach for an impinging Gaussian pulse of length TTT a detection probability of 84.5%84.5\%84.5% with a dark count rate of 10−3/T10^{-3}/T10−3/T, and promise to outperform competing schemes.
Quantum-enhanced sensing has a goal of enhancing a parameter sensitivity with input quantum states, while quantum illumination has a goal of enhancing a target detection capability with input entangled states in a heavy noise environment. Here we propose a concatenation between quantum-enhanced sensing and quantum illumination that can take quantum advantage over the classical limit. First, phase sensing in an interferometry is connected to a target sensing via quantum Fisher information. Second, the target sensitivity is investigated in noisy quantum-enhanced sensing. Under the same input state energy, for example, NNN-photon entangled states can exhibit better performance than a two-mode squeezed vacuum state and a separable coherent state. Incorporating a photon-number difference measurement, finally, the noisy target sensitivity is connected to a signal-to-noise ratio which is associated with a minimum error probability of discriminating the presence and absence of the target. We show that both the target sensitivity and the signal-to-noise ratio can be enhanced with increasing thermal noise.