Mapping Fields: Protocol Hides Source Locations with 100% Fidelity

Researchers are developing quantum sensing techniques to map magnetic fields with applications ranging from medical diagnostics to secure communication. Hiroto Kasai from the Graduate School of Pure and Applied Sciences, University of Tsukuba and the Graduate School of Science and Technology, Keio University, alongside Seiichiro Tani of the Department of Mathematics, Waseda University, Yasuhiro Tokura from the Graduate School of Pure and Applied Sciences, University of Tsukuba, and Yuki Takeuchi working with colleagues at NTT Communication Science Laboratories, NTT Corporation, NTT Research Center for Theoretical Quantum Information, NTT Corporation, and Information Technology R&D Center, Mitsubishi Electric Corporation, present a new anonymous sensing protocol that overcomes a critical limitation of existing methods. This work addresses the challenge of state preparation errors, which commonly occur in quantum systems and can compromise the privacy-preserving nature of anonymous sensing. By devising a novel state verification protocol based on Greenberger-Horne-Zeilinger and Dicke states, the team demonstrates improved robustness and fidelity estimation, paving the way for more reliable and secure magnetic field mapping in practical scenarios. A technique to safeguard sensitive data gathered by quantum sensors has been developed by scientists. The method ensures privacy when mapping magnetic fields, such as those produced by the human body, by concealing the source locations. This advance addresses a practical limitation of existing quantum sensing by tolerating imperfections in equipment. Networked quantum sensors are finding increasing applications in fields like magnetic field mapping. When these sensors detect biomagnetic fields, carrying private information, protecting the source of those signals from eavesdroppers becomes essential. Anonymous quantum sensing addresses this need by estimating magnetic field amplitudes without revealing the locations of their origin. This work introduces a new protocol for anonymous quantum sensing that remains effective even when initial quantum states are imperfect. Researchers developed a quantum state verification protocol to assess the quality of a superposition of Greenberger-Horne-Zeilinger and Dicke states, complex quantum states used in the sensing process. By integrating this verification step with existing anonymous sensing techniques, the system can confirm whether the prepared quantum states are sufficiently accurate for reliable operation. Previous anonymous sensing protocols were vulnerable to errors arising from imperfect state preparation, but this new protocol efficiently determines state fidelity, deciding if the actual states closely match the ideal ones with greater speed than traditional methods. This improvement lies in a novel approach to state verification, focusing on collapsing the complex multi-qubit state into simpler forms for more efficient assessment. By adaptively switching between established verification methods for these simpler states, the researchers achieved a substantial reduction in the number of samples needed to confirm state quality. This enhanced efficiency promises to improve the practical viability of anonymous quantum sensing, particularly in scenarios where maintaining privacy alongside accurate measurements is paramount. The research opens avenues for secure biomagnetic field mapping and other applications demanding both precision and confidentiality. State preparation errors, stemming from imperfections in equipment, can degrade performance. To overcome this, the team devised a method to verify the quality of these states before use in the sensing process. This verification protocol leverages the unique properties of a superposition of Greenberger-Horne-Zeilinger (GHZ) and Dicke states, crucial for achieving anonymity. By strategically measuring subsets of qubits in the Pauli-Z basis, the protocol efficiently determines if the prepared state is sufficiently close to the ideal state. The efficiency of this verification process is key, as direct fidelity estimation requires a number of samples that scales inversely with the square of the acceptable noise level. In contrast, the new protocol requires samples that scale inversely with the noise level alone, representing a considerable improvement, particularly when dealing with noisy quantum systems. Furthermore, the researchers explored the relationship between the sensitivity of the anonymous sensing protocol and the sample complexity of the verification protocol. This connection allows for fine-tuning of the system to optimise performance based on available resources. The core concept of anonymous quantum sensing relies on a cooperative effort between a distributor, multiple participants, and an observer. The distributor generates a symmetric quantum state, a superposition of GHZ and Dicke states, and distributes qubits to each participant. Each participant interacts their qubit with a local magnetic field before sending it to the observer, who performs measurements to estimate the field amplitudes without revealing the source. By employing symmetric states and measurements, the protocol ensures that the output probability distribution remains independent of the location of the magnetic field source, thus preserving anonymity. For a given noise threshold, the newly developed quantum state verification protocol requires fewer samples than traditional methods. The protocol’s efficiency stems from its ability to adaptively switch between existing verification protocols designed for simpler quantum states, allowing for a more targeted and efficient assessment of overall state quality. Beyond the technical advancements, this work has implications for a range of applications, including secure medical diagnostics and environmental monitoring, where preserving the privacy of sensitive data is paramount.

This research establishes a pathway toward building practical and secure quantum sensing networks. Reduced sampling complexity and noise resilience in quantum state verification Initial fidelity estimations revealed a clear distinction between high and low fidelity states with greater efficiency than direct estimation methods. Specifically, the devised quantum state verification protocol requires only O(ε−1) samples for a noise strength lower bound of ε, whereas direct fidelity estimation demands O(ε−2) samples. This represents a substantial reduction in the resources needed to assess state quality. Once a state’s fidelity is confirmed, the protocol enables more accurate amplitude estimation of magnetic fields, addressing a key limitation of previous anonymous sensing designs. The core advancement lies in the protocol’s resilience to independent noise during state preparation. By incorporating a verification step, the system circumvents the previously fatal flaw where state preparation errors would invalidate magnetic field amplitude estimations. This verification relies on collapsing a superposition of 2n-qubit Greenberger-Horne-Zeilinger and Dicke states into either an n-qubit GHZ-like state or a Dicke state through selective measurement of n qubits in the Pauli-Z basis. Adapting existing verification protocols for these simpler states then becomes possible. Analysis demonstrates a direct relationship between the sensitivity achieved in the anonymous quantum sensing and the sample complexity of the quantum state verification protocol. By varying a free parameter within the sensing protocol, researchers can fine-tune the balance between sensitivity and the number of samples required for verification. At a fundamental level, the work establishes a pathway toward practical implementation of secure, networked quantum sensors. The ability to accurately map biomagnetic fields while preserving anonymity is now closer to realisation. The protocol’s design allows for adaptive switching between established verification methods for GHZ-like and Dicke states, optimising efficiency. The system can effectively determine whether the fidelity between ideal and actual states is high or low, a process that previously demanded significantly more computational resources. Beyond the efficiency gains, this adaptive approach offers flexibility in handling varying levels of noise. By addressing the critical issue of state preparation errors, this work unlocks the potential of anonymous quantum sensing for real-world applications. The demonstrated improvements in fidelity estimation and resource efficiency represent a considerable step forward in the field of secure quantum networks. GHZ and Dicke state fidelity assessment via component decomposition A state verification protocol, designed for superposition states of Greenberger-Horne-Zeilinger and Dicke types, underpins the methodology of this work. Researchers focused on quantifying the GHZ-like component across all possible sets of qubits by calculating the expectation value of the Z0 operator. The study extended this analysis to include the Dicke component, mirroring the approach used for the GHZ-like component. By combining the contributions from both components, the researchers developed a comprehensive framework for verifying the overall quantum state. This framework relies on a summation over all possible qubit sets, allowing for a robust assessment of fidelity even in the presence of noise and imperfections. Since the protocol is designed to work with imperfect sources, it offers a practical advantage over methods that assume ideal conditions. Quantum state verification enhances privacy in anonymous magnetic field sensing Scientists are increasingly focused on secure data collection, and a new approach to anonymous sensing offers a potential step forward. For years, the challenge has been to gather information about the presence of a magnetic source without revealing its location. This is not merely a technical hurdle; it’s a fundamental requirement for protecting privacy. Previous methods struggled to maintain anonymity when faced with even minor imperfections in the sensing process, leaving data vulnerable to reconstruction. This work bypasses that limitation by incorporating a state verification protocol. By confirming the quality of the initial quantum state used for sensing, the system becomes far less susceptible to errors introduced during preparation. That allows for more accurate amplitude estimation of magnetic fields, even when the underlying technology isn’t perfect. Instead of demanding flawless equipment, the protocol adapts to real-world conditions, a pragmatic shift for practical applications. The computational cost of verifying the state could become significant as the network scales. The analysis relies on specific mathematical conditions, notably, a particular range for the parameter λ0, and it remains unclear how sensitive the protocol is to deviations from these ideal values. Once these parameters are better understood, the next step will be to explore how this approach integrates with existing sensor networks and data processing pipelines. The biggest question isn’t whether this method works in a lab, but whether it can be deployed cost-effectively and reliably in a real-world setting. For biomagnetic sensing, this could mean less invasive brain-computer interfaces or more accurate diagnostics. However, the broader implications extend to any application where privacy-preserving data collection is paramount, from environmental monitoring to smart city infrastructure. The path forward requires a move beyond theoretical gains and towards engineering solutions that bridge the gap between quantum promise and practical utility. 👉 More information 🗞 Anonymous quantum sensing robust against state preparation errors 🧠 ArXiv: https://arxiv.org/abs/2602.14396 Tags: