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Physical Review A

Quantum illumination with high-dimensional Bell states

Armanpreet Pannu, Amr Saher Helmy, Hesham El Gamal

Published Nov 25, 2024• 2 citations
Publisher

Abstract

This work explores a protocol for quantum illumination using high-dimensional Bell states, showing that discrete-variable states can be effective in detecting targets across different noise conditions. The findings suggest that Bell states may serve as a viable alternative to continuous-variable states in quantum sensing, expanding the possibilities for entanglement-enhanced applications.

DOI
10.1103/physreva.110.l050603

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This work explores a protocol for quantum illumination using high-dimensional Bell states, showing that discrete-variable states can be effective in detecting targets across different noise conditions. The findings suggest that Bell states may serve as a viable alternative to continuous-variable states in quantum sensing, expanding the possibilities for entanglement-enhanced applications.
This paper solves the open problem of characterizing the performance of quantum illumination (QI) with discrete variable states. By devising a novel quantum measurement approach along with meticulous analysis, our investigation demonstrates that, in the limit as M→∞M \rightarrow \inftyM→∞, the maximally entangled MMM mode Bell state achieves optimal performance, matching the two-mode squeezed vacuum in a high-noise regime and exceeding it in low-noise. This result challenges the dominance of continuous variable states in photonic sensing applications and extends the novelty of QI to regimes where no quantum advantage was believed to exist. A closer analysis reveals that this advantage stems from retained entanglement in the transmitted Bell state, a paradigm-shifting discovery since interaction with the environment in optical systems is believed to break entanglement. The complete mathematical analysis of this work provides granular insights into the interaction between photonic systems and environmental noise, motivating further research into discrete variable quantum sensing.
Quantum illumination is one of the application protocols of This protocol uses entanglement for target detection. The protocol was first proposed by Lloyd, and its performance was later studied by Tan et al. In a lossy environment, they considered a Gaussian state in the presence of thermal noise. Entanglement with nonorthogonal states, such as coherent states, produces These states have been shown to be capable of perfect entanglement. In this paper, we consider quantum illumination using quasi-Bell states, and compute the minimum error probability of quantum illumination under these states.
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.
Quantum illumination has been a hot topic in quantum sensing since first proposed by S. Lloyd in 2008. Quantum illumination is an entanglement-based protocol that is able to detect the existence of a target in an environment with low-energy transmissivity and strong thermal noise. The Bell state and the two-mode squeezed vacuum (TMSV) state as an entangled light source have been widely discussed. In our previous study, we clarified that quantum illumination using the quasi-Bell state offers good performance at error probability even though easing the above-mentioned restrictions on the environment. In this study, we considered and discussed a physical implementation of a measurement scheme for the quasi-Bell state-based quantum illumination using a beam splitter and photon counters. As the result, although the measurement scheme is not an optimum scheme, it still offers a clear advantage over that using the TMSV state, which allows optimum quantum detection, under almost situations.
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.