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Scientific Reports

Quantum loss sensing with two-mode squeezed vacuum state under noisy and lossy environment

Sang-il Park, Changsuk Noh, Changhyoup Lee

Published Apr 12, 2023• 12 citations
Publisher

Abstract

We investigate quantum advantages in loss sensing when the two-mode squeezed vacuum state is used as a probe. Following an experimental demonstration in PRX 4, 011049, we consider a quantum scheme in which the signal mode is passed through the target and a thermal noise is introduced to the idler mode before they are measured. We consider two detection strategies of practical relevance: coincidence-counting and intensity-difference measurement, which are widely used in quantum sensing and imaging experiments. By computing the signal-to-noise ratio, we verify that quantum advantages persist even under strong thermal background noise, in comparison with the classical scheme which uses a single-mode coherent state that directly suffers from the thermal noise. Such robustness comes from the fact that the signal mode suffers from the thermal noise in the classical scheme, while in the quantum scheme, the idler mode does. For a fairer comparison, we further investigate a different setup in which the thermal noise is introduced to the signal mode in the quantum schemes. In this new setup, we show that the quantum advantages are significantly reduced. Remarkably, however, under an optimum measurement scheme associated with the quantum Fisher information, we show that the two-mode squeezed vacuum state does exhibit a quantum advantage over the entire range of the environmental noise and loss. We expect this work to serve as a guide for experimental demonstrations of quantum advantages in loss parameter sensing, which is subject to lossy and noisy environment.

DOI
10.1038/s41598-023-32770-7

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We investigate quantum advantages in loss sensing when the two-mode squeezed vacuum state is used as a probe. Following an experimental demonstration in PRX 4, 011049, we consider a quantum scheme in which the signal mode is passed through the target and a thermal noise is introduced to the idler mode before they are measured. We consider two detection strategies of practical relevance: coincidence-counting and intensity-difference measurement, which are widely used in quantum sensing and imaging experiments. By computing the signal-to-noise ratio, we verify that quantum advantages persist even under strong thermal background noise, in comparison with the classical scheme which uses a single-mode coherent state that directly suffers from the thermal noise. Such robustness comes from the fact that the signal mode suffers from the thermal noise in the classical scheme, while in the quantum scheme, the idler mode does. For a fairer comparison, we further investigate a different setup in which the thermal noise is introduced to the signal mode in the quantum schemes. In this new setup, we show that the quantum advantages are significantly reduced. Remarkably, however, under an optimum measurement scheme associated with the quantum Fisher information, we show that the two-mode squeezed vacuum state does exhibit a quantum advantage over the entire range of the environmental noise and loss. We expect this work to serve as a guide for experimental demonstrations of quantum advantages in loss parameter sensing, which is subject to lossy and noisy environment.
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.
Nonclassical states are essential for optics-based quantum information processing, but their fragility limits their utility for practical scenarios in which loss and noise inevitably degrade, if not destroy, nonclassicality. Exploiting nonclassical states in quantum metrology yields sensitivity advantages over all classical schemes delivering the same energy per measurement interval to the sample being probed. These enhancements, almost without exception, are severely diminished by quantum decoherence. Here, we experimentally demonstrate an entanglement-enhanced sensing system that is resilient to quantum decoherence. We employ entanglement to realize a 20% signal-to-noise ratio improvement over the optimum classical scheme in an entanglement-breaking environment plagued by 14 dB of loss and a noise background 75 dB stronger than the returned probe light. Our result suggests that advantageous quantum-sensing technology could be developed for practical situations.
We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons N-S transmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of root 2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/N-S) larger than the optimal classical setup, in the N-S << 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.
We study a quantum-enhanced differential measurement scheme that uses quantum probes and single-photon detectors to measure a minute defect in the absorption parameter of an analyte under investigation. For the purpose, we consider two typical non-classical states of light as a probe, a twin-Fock state and a two-mode squeezed vacuum state. Their signal-to-noise ratios (SNRs) that quantifies the capability of detecting the defect are compared with a corresponding classical imaging scheme that employs a coherent state input. A quantitative comparison is made in terms of typical system imperfections such as photon loss and background noise that are common in practice. It is shown that a quantum enhancement in SNR can be described generally by the Mandel Q-parameter and the noise-reduction-factor, which characterize an input state that is incident to the analyte. We thereby identify the conditions under which the quantum enhancement remains and can be further increased. We expect our study to provide a guideline for improving the SNR in quantum imaging experiments employing a differential measurement scheme with time-integrated single-photon detectors.
Entanglement is beneficial to enhancing a phase sensitivity beyond the classical limit that is given by a coherent state. The best performance is achieved with symmetric entangled states, which is enhanced further by sending more photons to the signal mode. We delve into which entanglement structure is valuable for quantum target sensing, such as a reflectivity parameter. We show that an asymmetric entangled state can approach the local joint measurement bound of a two-mode squeezed vacuum state which is a nearly optimal input state for quantum target sensing, whereas it cannot beat the performance of the coherent state for quantum phase sensing. The result is demonstrated with an asymmetric entangled coherent state whose performance is evaluated with quantum Fisher information and confirmed by the signal-to-noise ratio with an optimal observable. The best quantum advantage is achieved in the case of sending fewer photons to the signal mode and many more photons to the idler mode.
We compare the performance of a quantum radar based on two-mode squeezed states with a classical radar system based on correlated thermal noise. With a constraint of equal number of photons NStransmitted to probe the environment, we find that the quantum setup exhibits an advantage with respect to its classical counterpart of √2 in the cross-mode correlations. Amplification of the signal and the idler is considered at different stages of the protocol, showing that no quantum advantage is achievable when a large-enough gain is applied, even when quantum-limited amplifiers are available. We also characterize the minimal type-II error probability decay, given a constraint on the type-I error probability, and find that the optimal decay rate of the type-II error probability in the quantum setup is ln(1 + 1/NS) larger than the optimal classical setup, in the NS<; <; 1 regime. In addition, we consider the Receiver Operating Characteristic (ROC) curves for the scenario when the idler and the received signal are measured separately, showing that no quantum advantage is present in this case. Our work characterizes the trade-off between quantum correlations and noise in quantum radar systems.