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Distributed multi-parameter quantum sensing based on Gaussian multipartite entanglement

Shuhong Hao, Dong Wang, Xutao Mo, Zhiyan Li, Jun Li

Published Jun 29, 2026• 0 citations
Publisher

Abstract

Distributed quantum sensing has important applications in quantum-enhanced estimation of global parameters, which is the weighted sum of each sensor. Towards applications, it is essential to estimate more global parameters simultaneously. Here, we propose an improved quantum-enhanced distributed multi-parameter sensing of more than two global parameters simultaneously via Gaussian multipartite entanglement. We show that two global parameters, containing the real and imaginary parts of the complex amplitudes of multiple radio-frequency fields, can be estimated based on an Einstein-Podolsky-Rosen entangled state. Compared to the distributed quantum sensing with squeezed light in the same sensing network, the sensors are extended from M to 2 M in the improved scheme with multipartite entanglement. This work provides a practical approach for advancing high-precision multi-parameter quantum sensing technologies.

DOI
10.1364/oe.592907

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Distributed quantum sensing has important applications in quantum-enhanced estimation of global parameters, which is the weighted sum of each sensor. Towards applications, it is essential to estimate more global parameters simultaneously. Here, we propose an improved quantum-enhanced distributed multi-parameter sensing of more than two global parameters simultaneously via Gaussian multipartite entanglement. We show that two global parameters, containing the real and imaginary parts of the complex amplitudes of multiple radio-frequency fields, can be estimated based on an Einstein-Podolsky-Rosen entangled state. Compared to the distributed quantum sensing with squeezed light in the same sensing network, the sensors are extended from M to 2 M in the improved scheme with multipartite entanglement. This work provides a practical approach for advancing high-precision multi-parameter quantum sensing technologies.
Quantum sensing has emerged as a promising solution for precision measurement, and distributed quantum sensing enables multiple parameters to be measured across a network. Pushing distributed quantum sensing from the single to multimodal parameters is crucial for a complete and deep understanding of a complex system. To address this challenge, we have devised a high-sensitivity distributed quantum sensing of the multimodal parameters with a continuous-variable multipartite Greenberger–Horne–Zeilinger entangled state. All the sensors are equipped with Mach–Zehnder interferometers to couple the lasers with entangled modes. In such a quantum network, not only joint but also individual measurements of radio frequency phases and amplitudes as well as ultrasonic vibration signals are achieved beyond the standard quantum limit, showcasing the quantum Fisher information of the order of 10 16 . These results render multimodal parameters a promising contender in quantum metrology.
Distributed quantum sensing uses quantum correlations between multiple sensors to enhance the measurement of unknown parameters beyond the limits of unentangled systems. We describe a sensing scheme that uses continuous-variable multipartite entanglement to enhance distributed sensing of field-quadrature displacement. By dividing a squeezed-vacuum state between multiple homodyne-sensor nodes using a lossless beam-splitter array, we obtain a root-mean-square (rms) estimation error that scales inversely with the number of nodes (Heisenberg scaling), whereas the rms error of a distributed sensor that does not exploit entanglement is inversely proportional to the square root of the number of nodes (standard quantum limit scaling). Our sensor's scaling advantage is destroyed by loss, but it nevertheless retains an rms-error advantage in settings in which there is moderate loss. Our distributed sensing scheme can be used to calibrate continuous-variable quantum key distribution networks, to perform multiple-sensor cold-atom temperature measurements, and to do distributed interferometric phase sensing.
Distributed quantum sensing, which estimates a global parameter across distant nodes, has attracted significant interest for applications such as quantum imaging, sensor networks, and global-scale clock synchronization. N00N states are regarded as one of the optimal quantum resources for quantum metrology, enabling the Heisenberg scaling. Recently, the concept of N00N states has been extended to multimode N00N states for quantum-enhanced multiple-parameter estimation. However, the application of multimode N00N states in distributed quantum sensing remains unexplored. Here, we propose a distributed quantum sensing scheme that achieves the Heisenberg scaling using multimode N00N states. We theoretically show that multimode N00N states can reach the Heisenberg scaling by examining both the Cramér-Rao bound and the quantum Cramér-Rao bound. For experimental demonstration, we employ a four-mode 2002 state to estimate the average of two spatially distributed phases, achieving a 2.74 dB sensitivity enhancement over the standard quantum limit. We believe that utilizing multimode N00N states for distributed quantum sensing offers a promising approach for developing entanglement-enhanced sensor networks.
Abstract A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like 1 / M . However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.
This paper investigates the potential of multi-parameter quantum state control for enhancing the performance of quantum sensors. The core claim centers on leveraging precisely controlled quantum states to achieve highly accurate measurements of multiple physical parameters simultaneously. The proposed mechanism involves manipulating quantum states with multiple parameters, allowing for correlated measurements and improved sensitivity. This work explores theoretical frameworks and outlines a strategy for developing quantum sensors that benefit from this approach. The paper focuses on the design principles and challenges associated with implementing such a system, emphasizing the role of quantum entanglement and coherence in achieving high precision. The ultimate goal is to demonstrate how multi-parameter quantum state control can unlock new possibilities for quantum sensing applications, particularly in areas demanding simultaneous measurement of diverse physical quantities. This research contributes to the growing field of quantum sensing by proposing a novel method that could significantly improve sensor accuracy and expand its capabilities.
Quantum sensing is a major branch of quantum information technology that uses the principles of quantum mechanics to achieve enhanced precision and accuracy for parameter estimation and hypothesis testing problems. This paper presents a Gaussian quantum states-based quantum sensing paradigm. Gaussian quantum states have the advantage of being relatively easy to generate and manipulate in practice, and they can be used for realizing quantum sensors in the near term. Squeezed quantum states which are an example of Gaussian quantum states can improve the estimation accuracy by reducing the quantum shot noise in one of the quadratures. We present two prototypical examples of Gaussian states-based quantum sensing applications, including quadrature estimation and channel transmittance estimation of a lossy bosonic Gaussian channel. We show that improved estimation can be achieved for both problems by using squeezed states compared to classical coherent states.