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arXiv:2205.06382 · Nature

Distributed quantum sensing with mode-entangled spin-squeezed atomic states

Benjamin K. Malia, Yunfan Wu, Julián Martínez-Rincón, Mark A. Kasevich

Published Nov 23, 2022• 121 citations
arXivHTMLPDF
DOI
10.1038/s41586-022-05363-z

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Recent developments in quantum technologies have enabled significant improvements in the precision of optical sensing systems. This work explores the integration of distributed quantum sensing with optical gyroscopes to improve the estimation accuracy of angular velocity. Utilizing bright two-mode squeezed states (bTMSS), which offer high photon numbers and strong bipartite quantum correlations, we propose a configuration that leverages continuous-variable entanglement across multiple spatially separated optical gyroscopes. Unlike traditional quantum sensing that enhances a single sensor, our approach focuses on estimating a global phase shift—corresponding to the average angular rotation—across distributed optical gyroscopes with quantum-enhanced sensitivity. We analyze the phase sensitivities of different bTMSS configurations, including mode entangled bTMSS and separable M -bTMSS, and evaluate their performance through the quantum Cramér-Rao bound. The analysis shows that, with 5 % photon loss in every channel in the system, the proposed scheme shows a sensitivity enhancement of ∼ 9.3 dB beyond the shot-noise limit, with an initial squeezing of ∼ 9.8 dB . The present scheme has potential applications in quantum-enhanced inertial navigation and precision metrology within emerging quantum networks.

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In ``Distributed quantum sensing with mode-entangled spin-squeezed atomic states" Nature (2022), Malia et. al. claim to improve the precision of a network of clocks by using entanglement. In particular, by entangling a clock network with up to four nodes, a precision 11.6 dB better than the quantum projection noise limit (i.e. precision without any entanglement) is reported. These claims are incorrect, Malia et. al. do not achieve an improved precision with entanglement. Here we show their demonstration is more than two orders of magnitude worse than the quantum projection noise limit.
Abstract We identify the multiparameter sensitivity of entangled spin states, such as spin-squeezed and Dicke states that are spatially distributed into several addressable spatial modes. Analytical expressions for the spin-squeezing matrix of families of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity gain for the estimation of any linear combination of parameters. We further study the mode entanglement of these states by deriving a witness for genuine k-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles. We illustrate our findings with the design of a protocol for gradient sensing with a Bose–Einstein condensate in an entangled spin state in two modes.
Distributed quantum sensing is an emerging application of quantum networking, where entangled probe states are employed to sense combinations of delocalized parameters with enhanced precision relative to using separable states. Squeezed states of light are a prime resource for experimental demonstrations of entanglement-enhanced sensing, because they can be generated and entangled deterministically. Existing distributed quantum sensing experiments have been fundamentally limited in scalability due to their bulk-optic architectures. Meanwhile, integrated photonics provides a scalable and compact platform for quantum sensors. Here we demonstrate entanglement-enhanced sensing of linear functions of four phase shifts in an integrated photonic circuit. We find an entanglement-enhanced precision of 0.199(16) dB below the shot noise limit compared to 0.041(18) dB for separable states. A four-mode entangled state is generated on-chip with entanglement verification and phase sensing also performed on-chip with an array of four integrated homodyne detectors.
Recent developments in quantum technologies have enabled significant improvements in the precision of optical sensing systems. This work explores the integration of distributed quantum sensing with optical gyroscopes to improve the estimation accuracy of angular velocity. Utilizing bright two-mode squeezed states (bTMSS), which offer high photon numbers and strong bipartite quantum correlations, we propose a configuration that leverages continuous-variable entanglement across multiple spatially separated optical gyroscopes. Unlike traditional quantum sensing that enhances a single sensor, our approach focuses on estimating a global phase shift—corresponding to the average angular rotation—across distributed optical gyroscopes with quantum-enhanced sensitivity. We analyze the phase sensitivities of different bTMSS configurations, including mode entangled bTMSS and separable M -bTMSS, and evaluate their performance through the quantum Cramér-Rao bound. The analysis shows that, with 5 % photon loss in every channel in the system, the proposed scheme shows a sensitivity enhancement of ∼ 9.3 dB beyond the shot-noise limit, with an initial squeezing of ∼ 9.8 dB . The present scheme has potential applications in quantum-enhanced inertial navigation and precision metrology within emerging quantum networks.