All-optical Loss-tolerant Distributed Quantum Sensing

npj | quantum information Article Published in partnership with The University of New South Wales https://doi.org/10.1038/s41534-025-01123-9 All-optical Loss-tolerant Distributed Quantum Sensing Check for updates 1234567890():,; 1234567890():,; Rajveer Nehra1,2,3,4,7 , Changhun Oh5,6,7 , Liang Jiang5 & Alireza Marandi1 Distributed quantum sensing (DQS) leverages quantum resources to estimate an unknown global property of a networked quantum sensor beyond the classical limit. We propose and analyze an alloptical resource-efficient scheme for the next-generation DQS systems. Our method utilizes phasesensitive optical parametric amplifiers (OPAs) and linear interferometers and achieves the sensitivity close to the optimal limit, as determined by the quantum Fisher information of the entangled resource state. Furthermore, it utilizes high-gain OPA-assisted detection, offering critical advantages of increased bandwidth and loss tolerance, in contrast to conventional methods employing balanced homodyne detection (BHD). We show the efficacy of our proposal for displacement sensing and show its loss tolerance against high levels of photon loss, thus circumventing the major obstacle in current BHD-based approaches. Our architectural analysis shows that our scheme can be realized with current quantum photonic technology. Quantum metrology estimates an unknown physical quantity using quantum resources beyond what is allowed by classical counterparts1–3. Since the first proposal of using quantum resources to enhance the gravitational-wave detection by squeezed states4, there have been numerous theoretical proposals and proof-of-principle experiments, including quantum-enhanced interferometer and quantum-enhanced clock5–14. Displacement sensing15, in particular, has attracted much attention due to its various potential applications in fundamental sciences and the development of novel sensing technologies. These applications include force sensing16–18, dark matter search19–21, and enhanced radio-frequency signal detection22. Conventional displacement sensing involves estimating the displacement of an input state in continuous phase space, assuming a prior knowledge of the displacement axis. The optimal measurement scheme in such scenarios is balanced homodyne detection (BHD), which measures the phase-space quadratures along the known displacement axis23. Even when extending displacement sensing to distributed displacement sensing, which involves estimating a global quantity in distant quantum nodes, homodyne detection remains the most suitable measurement scheme in such schemes with continuous variable (CV) systems22,24,25. Moreover, recently developed machine learning-assisted entangled sensor network architectures also make use of BHD to enhance the sensitivity of the global parameters26,27. While these tabletop experiments have shown quantum-enhanced precision, their performance is significantly limited than the expected advantages offered by quantum entanglement22,27. The degraded performance is mostly attributed to the overall detection inefficiency of quadrature measurements obtained with BHD28. Additionally, the BHD detectors have a restricted bandwidth within the megahertz-to-gigahertz range, which limits their ability to access the terahertz bandwidth of quantum fields for distributed sensing28,29. On the other hand, distributed quantum sensing (DQS) systems with discrete variable encoding offer limited improvements due to their inherent probabilistic nature and slow performance of superconducting single-photon detectors, which require complex cryogenic operations posing significant scalability challenges22,30. In this work, we introduce a novel approach that overcomes the limitations of traditional BHD-based distributed sensors with CV systems. Our approach involves the utilization of phase-sensitive optical parametric amplifiers (OPAs) to generate and measure squeezed states, in addition to employing simple linear optics. As a result, it exhibits high tolerance to the photon loss in the measurement, which is crucial to achieving quantum advantages. Moreover, it significantly expands the accessible bandwidth of quantum fields to tens of terahertz, offering significant scalability advantages. It is worth emphasizing that the preamplification in the optical domain offers tolerance against the LO phase noise and limited commonmode rejection ratio in conventional BHD schemes. Furthermore, it improves the shot noise to electronic noise clearance, leading to higher overall detection efficiency. We show that by adjusting the measurement 1 Department of Electrical Engineering, California Institute of Technology, Pasadena, CA, USA. 2Department of Electrical and Computer Engineering, University of Massachusetts Amherst, Amherst, MA, USA. 3Department of Physics, University of Massachusetts Amherst, Amherst, MA, USA. 4College of Information and Computer Science, University of Massachusetts Amherst, Amherst, MA, USA. 5Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL, USA. 6Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea. 7These authors contributed equally: Rajveer e-mail: ; ; ; Nehra, Changhun Oh. npj Quantum Information | (2026)12:18 1 Article https://doi.org/10.1038/s41534-025-01123-9 Fig. 1 | Comparison between conventional homodyne detection and the proposed all-optical measurement using high-gain optical parametric amplifiers (OPAs). a Conventional balanced homodyne measurement for quadratures on a quantum state ^ρ. Here, LO stands for local oscillator. b Proposed all-optical measurement for squared quadratures. When the gain is large G ≫ 1, The photocurrent operator, ^I, is proportional to the photon number operator, which is primarily determined by the amplified squared quadrature ^x2ϕ , as given by Eq. (3). Note that for practical implementation, we measure the intensity of the output state after the OPA rather than resolving individual photon numbers. parameters, our approach achieves near-optimal performance determined by the quantum Fisher information (QFI) of the probe states. The structure of our paper is as follows: Measurement scheme details all-optical loss-tolerant measurements using high-gain phase-sensitive OPAs. Subsequently, Single-mode displacement sensing and Multi-mode distributed displacement sensing present a comprehensive analysis of single-mode and multi-mode displacement sensing. Experimental prospects delves into the experimental prospects of our scheme. Finally, in Discussion, we conclude our findings and provide an outlook for future research. Measurement scheme This section describes our measurement scheme with high-gain phasesensitive OPA, as opposed to BHD for single-mode and multi-mode distributed displacement sensing in traditional DQS systems. As depicted in Fig. 1, BHD involves mixing a weak quantum field with a relatively strong well-calibrated local oscil (...truncated)