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Photonics Research

Quantum positioning and ranging via a distributed sensor network

Xiaocong Sun, Wei Li, Yuhang Tian, Fan Li, Long Tian, Yajun Wang, Yaohui Zheng, Kunchi Peng

Published Oct 28, 2022• 18 citations
Publisher

Abstract

A quantum sensor network with multipartite entanglement offers a sensitivity advantage in optical phase estimation over the classical scheme. To tackle richer sensing problems, we construct a distributed sensor network with four nodes via four partite entanglements, unveil the estimation of the higher order derivative of radio-frequency signal phase, and unlock the potential of quantum target ranging and space positioning. Taking phased-array radar as an example, we demonstrate the optimal quantum advantages for space positioning and target ranging missions. Without doubt, the demonstration that endows innovative physical conception opens up widespread application of quantum sensor networks.

DOI
10.1364/prj.469166

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Radar Sensor Technology•May 4, 2020•0 citations
A quantum sensor network with multipartite entanglement offers a sensitivity advantage in optical phase estimation over the classical scheme. To tackle richer sensing problems, we construct a distributed sensor network with four nodes via four partite entanglements, unveil the estimation of the higher order derivative of radio-frequency signal phase, and unlock the potential of quantum target ranging and space positioning. Taking phased-array radar as an example, we demonstrate the optimal quantum advantages for space positioning and target ranging missions. Without doubt, the demonstration that endows innovative physical conception opens up widespread application of quantum sensor networks.
Quantum metrology takes advantage of nonclassical resources such as squeezing and entanglement to achieve a sensitivity level below the standard quantum limit (SQL). To date, most demonstrations of quantum sensing are restricted to a single sensor, nevertheless, many sensing tasks rely on an array of sensors working collectively. The measurement sensitivity of separable sensors scales as 1/sqrt(M) known as the SQL where M is the number of sensors. Shared entanglement among all sensors can be harnessed to surpass the SQL. Recent theoretical advances in distributed quantum sensing have shown that multipartite entangled states give rise to an improvement of 1/sqrt(M) in measurement sensitivity over separable states when estimating a global parameter. We develop a reconfigurable entangled sensor network based on continuous variable multipartite entangled states. The demonstrated entangled sensor network is composed of three sensor nodes, each equipped with an electro-optic transducer for the detection of radio-frequency (RF) signals. By properly tailoring the entangled states through a variational quantum circuit (VQC), the entangled sensor network can be reconfigured to minimize the measurement noise by more than 3dB below the SQL in different distributed RF sensing tasks, e.g., measuring the angle of arrival and mean amplitude of incident RF waves. Such a capability of capturing global features of interrogating objects by a reconfigurable entangled sensor network with less quantum noise further creates opportunities to enable a quantum advantage in data-processing problems. VQCs in conjunction with classical processing constitutes a promising architecture for quantum simulations, classical optimization, and machine learning. We train the VQC by classical machine learning algorithms to optimize the entanglement shared by the sensors for solving practical data processing problems. We show an entanglement-enabled reduction in error probability for classification of multidimensional RF signals. Our work establishes the quantum advantage of distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and data processing.
Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrology demonstrations are restricted to improving the measurement performance at a single sensor, but a plethora of applications require multiple sensors that work jointly to tackle distributed sensing problems. Here, we propose and experimentally demonstrate a reconfigurable sensor network empowered by continuous-variable (CV) multipartite entanglement. Our experiment establishes a connection between the entanglement structure and the achievable quantum advantage in different distributed sensing problems. The demonstrated entangled sensor network is composed of three sensor nodes each equipped with an electro-optic transducer for the detection of radio-frequency (RF) signals. By properly tailoring the CV multipartite entangled states, the entangled sensor network can be reconfigured to maximize the quantum advantage in distributed RF sensing problems such as measuring the angle of arrival of an RF field. The rich physics of CV multipartite entanglement unveiled by our work would open a new avenue for distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and timing.
Quantum sensor networks promise precision advantages over classical and single-sensor strategies, in particular when the estimator is non-local. We address the problem of finding such estimators through a framework we connote spatial quantum sensing: given an underlying field interrogated by a network of quantum sensors at fixed positions, construct an estimator for a property of the field, for example, distinguishing a source of signal, or evaluating the field or its derivatives at an arbitrary point. We first treat polynomial fields, casting the task as an interpolation problem, and then generalize to fields modeled by analytic functions, which yields general least-squares estimators. A central and largely unaddressed question is under what conditions on sensor placement these estimators are well-defined and error-free. For mmm-dimensional arrays we give explicit constructions and proofs in the interpolation setting using algebraic geometry, and establish necessary and sufficient conditions in the general case. Comparing a non-local entangled protocol with the best local strategy, we show that entanglement yields maximal precision in distributed sensing under global resource constraints. Finally, we introduce error-free subspaces, a technique that translates prior knowledge of the field into a reduction in the number of required sensors. We expect these techniques to be broadly useful in sensing problems across scales, ranging from earth-scale experiments to local applications such as biological imaging.
Quantum metrology takes advantage of nonclassical resources such as entanglement to achieve a sensitivity level below the standard quantum limit. To date, almost all quantum-metrology demonstrations are restricted to improving the measurement performance at a single sensor, but a plethora of applications require multiple sensors that work jointly to tackle distributed sensing problems. Here, we propose and experimentally demonstrate a reconfigurable sensor network empowered by continuous-variable (CV) multipartite entanglement. Our experiment establishes a connection between the entanglement structure and the achievable quantum advantage in different distributed sensing problems. The demonstrated entangled sensor network is composed of three sensor nodes each equipped with an electro-optic transducer for the detection of radiofrequency (RF) signals. By properly tailoring the CV multipartite entangled states, the entangled sensor network can be reconfigured to maximize the quantum advantage in distributed RF sensing problems such as measuring the angle of arrival of an RF field. The rich physics of CV multipartite entanglement unveiled by our work would open a new avenue for distributed quantum sensing and would lead to applications in ultrasensitive positioning, navigation, and timing.
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 Sensor Networks are often implemented to overcome some of the challenges presented by a single monostatic sensor system. In this paper we consider the possibility of geographically-distributed quantum radar nodes for improved target detection. Our theoretical design assumes N quantum sensor nodes with transmit-detect capabilities. One of these nodes is chosen to an “entangler node”, which generates entangled photon pairs and uses quantum channels to transmit, swap or teleport the photons to nodes A and B. One of the nodes retains the photon as an idler while the other transmits its photon as the signal. When this process is repeated across several nodes, there is a clear advantage of having different bearing angles to the target among the N nodes. Furthermore, the position and orientation of these sensor nodes could be actively optimized to maximize information about the state of the target. In addition, because the photon frequencies can be chosen to be independent of N, the system generates virtual modes that increase the performance of a single quantum sensor. The proposed design could be generalized to maintain the equivalent of a distributed quantum register among the N nodes so that the sharing of classical information from the detection among the nodes can permit state estimation to be performed in a completely uniform and consistent way. More specifically, each node receives a signal photon which is compared to its idler photon to produce something that relates to the state of the target but is completely non-informative to the individual nodes. It is only when the quantum information from the nodes is received at a secure central node that a full estimate comprising all information about the target from all nodes can be constructed. As we will discuss, the system not only is more information-efficient but also provides a certain level of security because any classical information leakage at a node (i.e., compromised by an adversary) will not actually reveal anything about the state of the target. Therefore, a set of geographically distributed quantum sensors can be treated as a single logical quantum radar device.