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Physical Review A

Asymmetric entanglement for quantum target sensing

Su‐Yong Lee, Jihwan Kim, Zaeill Kim, Duk Y. Kim

Published Apr 30, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.109.042429

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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.
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.
We study quantum phase sensing with asymmetric two-mode entangled coherent states (ECSs) in which the two local amplitudes take different values. We find the asymmetry-enhanced phase-sensing phenomenon in which the phase-sensing sensitivity is enhanced with increasing the asymmetry in the ECSs. We indicate that the phase-sensing sensitivity can attain and even surpass the Heisenberg limit in certain regimes of parameters. We further study the effect of decoherence induced by photon loss on the phase-sensing sensitivity. It is shown that the asymmetric ECSs have greater capability against decoherence compared with the symmetric ECSs. It is indicated that the asymmetric ECSs have significant advantages over the symmetric ECSs in quantum phase sensing. We also study the practical phase-sensing scheme with the intensity-difference measurement and show that the asymmetry in the asymmetric ECSs can enhance the phase sensitivity in the practical phase-measurement scheme. Our work reveals the asymmetry in the asymmetric ECSs is a resource for quantum-enhanced sensing and may be applied to ultrasensitive quantum phase sensing in the presence of photon loss.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
Quantum illumination is a quantum sensing protocol primarily used for object detection, which aims to detect the presence of a target with low reflectivity in the free space using quantum light fields. Here we investigate a quantum illumination scheme using an entangled light source by performing non-Gaussian operations on the two-mode squeezed vacuum (TMSV) state in order to reduce the detection error probability and meanwhile improve the signal-to-noise (SNR) ratio. We demonstrate that under the same squeezing parameter, the non-Gaussian operations can significantly reduce the detection error rate compared with the original TMSV state. Under the same average signal photon number, both the TMSV states with and without non-Gaussian operations can provide smaller error rate than that of the coherent state. In addition, we consider the balanced homodyne detection on idler and return signal photons as joint measurement and find that non-Gaussian operations can enhance the SNR of target detection by about 6--9 dB compared with that using TMSV. These results here demonstrate the advantage of the non-Gaussian entangled source in quantum illumination protocol and can find potential applications in target detection in noisy environment.
Quantum radar is a remote sensing technique for target detection that has extensively been explored in conjunction with entangled two-mode squeezed vacuum states. This work extends the existing protocol to a scheme that utilizes a three-mode squeezed state with genuine tripartite entanglement. The three entangled modes are divided into two signal modes and one idler mode. A numerical evaluation of the Chernoff bound shows that the proposed protocol has the potential to offer a higher quantum advantage in specific parameter regimes.
We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decreases with more loss in the interferometry. Under the constraint of the input mean photon number, we obtain that the optimal entangled coherent state is more robust than a separable coherent state, even in a high photon loss rate. The optimal entangled coherent state preserves quantum advantage over the standard interferometric limit of the separable coherent state. We also show that the corresponding optimal measurement requires correlation measurement bases.