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IEEE International Radar Conference

Configuration-Dependent Characteristics of Virtual-Mode Quantum Sensing Systems

Marco O. Lanzagorta, Jeffrey K. Uhlmann

Published Apr 1, 2020• 1 citation
Publisher

Abstract

Previous works have examined the use of a distributed network of quantum illumination and sensing nodes to augment the available number of distinguishable modes with an additional set of virtual modes. It has been shown that this approach in theory can be applied to achieve a required level of target detection performance within the constraints imposed by the limited rate at which entangled microwave photons can be generated. In this paper we examine how this performance is impacted by the spatial geometry of the network of nodes with respect to the target's range and cross section.

DOI
10.1109/radar42522.2020.9114856

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Previous works have examined the use of a distributed network of quantum illumination and sensing nodes to augment the available number of distinguishable modes with an additional set of virtual modes. It has been shown that this approach in theory can be applied to achieve a required level of target detection performance within the constraints imposed by the limited rate at which entangled microwave photons can be generated. In this paper we examine how this performance is impacted by the spatial geometry of the network of nodes with respect to the target's range and cross section.
Quantum sensing offers theoretical advantages over traditional classical alternatives. In the case of active radio- frequency quantum sensors, however, there exist several practical challenges, the most significant of which is the fast and efficient generation of a large number of entangled microwave photons. In a previous paper we proposed a method, called virtual modes, for mitigating this limitation by using a distributed architecture of quantum sensor units to synthetically increase the effective number of distinguishable modes available for target detection. Although this architecture was shown to incur an increase in noise cross-contamination, we showed that judicious sensor configurations can mitigate this effect. In this paper we examine more sophisticated cross-noise statistical models that permit the number and spatial distribution of sensors to be optimized to further reduce the net detection error probability of the proposed approach.
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.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.
In covert target detection, Alice attempts to send optical or microwave probes to determine the presence or absence of a weakly reflecting target embedded in thermal background radiation within a target region, while striving to remain undetected by an adversary, Willie, who is co-located with the target and collects all light that does not return to Alice. We formulate this problem in a realistic setting and derive quantum-mechanical limits on Alice's error probability performance in entanglement-assisted target detection for any fixed level of her detectability by Willie. We demonstrate how Alice can approach this performance limit using two-mode squeezed vacuum probes in the regime of small to moderate background brightness, and how such protocols can outperform any conventional approach using Gaussian-distributed coherent states. In addition, we derive a universal performance bound for nonadversarial quantum illumination without requiring the passive-signature assumption.
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.