Experimental distributed quantum sensing in a noisy environment

Abstract: The precision advantages offered by harnessing the quantum states of sensors can be readily compromised by noise. However, when the noise has a different spatial function than the signal of interest, recent theoretical work shows how the advantage can be maintained and even significantly improved. In this work we experimentally demonstrate the associated sensing protocol, using trapped-ion sensors. An entangled state of multi-dimensional sensors is created that isolates and optimally detects a signal, whilst being insensitive to otherwise overwhelming noise fields with different spatial profiles over the sensor locations. The quantum protocol is found to outperform a perfect implementation of the best comparable strategy without sensor entanglement. While our demonstration is carried out for magnetic and electromagnetic fields over a few microns, the technique is readily applicable over arbitrary distances and for arbitrary fields, thus present a promising application for emerging quantum sensor networks.

• The paper experimentally demonstrates a distributed quantum sensing protocol using entangled trapped-ion sensors for precise signal detection in noisy environments.
• It employs decoherence-free subspaces to achieve a quadratic precision advantage, outperforming non-entangled methods by a factor of 2.6.
• The study highlights the potential for scalable quantum sensor networks, paving the way for improved applications in geophysics, navigation, and secure communications.

Evaluating Experimental Distributed Quantum Sensing Protocols in Noisy Environments

This paper presents an experimental validation of a novel protocol for distributed quantum sensing, demonstrating the utility of entangled quantum states among multi-dimensional sensors when detecting signals in noisy environments. The authors leverage decoherence-free subspaces (DFSs) to effectively isolate the signal of interest from noise, thus providing a quantum advantage over classical and non-entangled approaches.

Overview of Methodology and Experimental Setup

The research utilizes trapped-ion sensors to create entangled states designed to be resilient against specific spatial noise profiles. The quantum protocol is specifically tested for magnetic and electromagnetic fields across a small scale, yet it shows promise for applications across arbitrary distances and field types, suggesting it could be a foundational tool in the development of quantum sensor networks.

Achieving a quadratic precision advantage is a notable capability of quantum sensors, particularly when the noise is of a different spatial form compared to the signal. In practical terms, this means that even when surrounded by non-ideal conditions, such as fluctuating electromagnetic fields, the entangled states enable more precise field measurements than the best possible scenario without entanglement.

Experimental Details and Results

The researchers set up an experiment using three $^{40}$Ca$^+$ trapped-ion sensors, spaced 4.9 µm apart, to target quadratic spatial dependencies in fields and remove influences from constant and linear fields. This experiment involved the use of both constant and gradient noise fields generated by external coils and controlled via custom noise profiles. The phase coherence between these ions acts as the measurable element, with the findings showing that the entangled states provided superior resistance to these noise fields compared to non-entangled states.

The authors provide quantitative results that support these conclusions: the entangled sensor state recorded an improved performance over both the experimental and theoretical separable scenarios, outperforming them by a factor of 2.6. This translates directly into an effective noise resilience, making it a robust method for scenarios plagued by fluctuations across various spatial profiles of field strengths. In essence, even when exposed to heavy noise, the DFS strategy rendered a significantly lower measurement error than the optimal separable (non-entangled) protocol.

Theoretical and Practical Implications

Theoretically, the research has demonstrated an exponential advantage in the use of the SWD protocol across higher-order Taylor expansions as noise profiles become more complex. Practically, this research establishes distributed quantum sensing as a viable and superior alternative for next-gen sensor networks, capable of significant improvements over current non-entangled methodologies.

This study opens several avenues for enhancing distributed quantum sensing. Integrated sensor environments with even more complex configurations and longer distances between sensors could exploit this resilience to noise, leading to improvements in fields ranging from geophysics to advanced navigation systems. Moreover, considering that this entanglement protocol can be generalized beyond confined ion-trap setups, its application to optical and solid-state systems offers promising directions for scalable quantum technology.

Future research and development should focus on integrating this approach over larger distances and increasing entanglement dimensions among sensor nodes, potentially driving innovation in global quantum networks and applications sensitive to electromagnetic interference. Such advances may hold particular significance in emerging technological deployments that require unprecedented precision, like those in astrophysics or secure communication networks.

In conclusion, this paper substantiates the quantum-enhanced approach for distributed sensing, rendering it an effective strategy in overcoming spatial noise—a persistent limitation in classical sensor networks. Through careful experimentation and application of DFSs, the authors successfully illuminate the path ahead for theoretical exploration and practical exploitation of quantum advantages in real-world sensor networks.