Quantum Metrology Achieves Heisenberg Scaling with 1/N Precision for Two-Channel Interferometry

The precise measurement of multiple parameters simultaneously represents a significant challenge in quantum metrology, yet achieving optimal precision is crucial for technologies ranging from sensing to imaging. Atmadev Rai from the University of Portsmouth, Danilo Triggiani from Politecnico di Bari, Paolo Facchi from Università di Bari, and Vincenzo Tamma from the University of Portsmouth, demonstrate a new framework for estimating all four parameters defining a two-channel optical interferometer with unprecedented accuracy. Their work establishes that Heisenberg-scaling precision, the theoretical limit of measurement accuracy, is achievable using readily available resources such as squeezed light, and provides concrete design principles for building advanced optical interferometers. This breakthrough not only deepens our understanding of how squeezed light enhances multiparameter estimation, but also paves the way for developing a new generation of technologies based on distributed quantum networks.

They derive analytical expressions for the quantum Fisher information and demonstrate that all parameters achieve precision scaling inversely with the number of measurements, using experimentally feasible Gaussian probes like two-mode or single-mode squeezed states. This work extends multiparameter metrology to its most general two-mode setting and establishes concrete design principles for implementing Heisenberg-scaling, multi-parameter optical interferometry with readily available resources.

Multi-Parameter Estimation with Squeezed Quantum States

This research focuses on quantum metrology, the use of quantum phenomena to improve measurement precision beyond classical limits. A key area of investigation is multi-parameter estimation, where the goal is to simultaneously determine multiple parameters, a significantly more challenging task than single-parameter estimation. Researchers explore the use of squeezed states, non-classical states of light where uncertainty in one property is reduced, to achieve Heisenberg-limited precision, the ultimate limit in quantum mechanics. The research considers fundamental limits on measurement precision, such as the Cramér-Rao bound, and addresses the challenges of probe incompatibility, where the optimal quantum state for estimating one parameter differs from that of another.

Gaussian states are often used due to their ease of generation and manipulation, but may not always achieve the Heisenberg limit. Researchers also investigate bounds on precision, including the Holevo, SLD, and RLD bounds. The work emphasizes the trade-offs inherent in multi-parameter estimation and the importance of carefully designing the initial quantum state, known as the probe state. Entanglement can enhance precision, but is not always necessary. Practical considerations, such as noise and imperfections, are also addressed. Researchers successfully demonstrated that by employing experimentally feasible Gaussian probe states, such as two-mode or single-mode squeezed states, it is possible to achieve this enhanced precision in parameter estimation. The analysis establishes concrete design principles for experiments aiming to reach this Heisenberg limit, paving the way for improved optical interferometry. The team’s findings highlight the necessity of displacement in the probe states, alongside squeezing, to simultaneously achieve Heisenberg-scaling precision for each parameter.

This detailed analysis, grounded in the quantum Cramér-Rao bound, provides a benchmark for designing experiments that maximize precision in characterizing linear optical interferometers. The results are expected to facilitate the development of scalable quantum technologies with applications in diverse fields, including quantum gate characterization, quantum imaging, biomedical sensing, and gravitational wave detection. The authors acknowledge that extending these results to systems with a larger number of channels represents a future research direction. Furthermore, they note that the practical implementation of these techniques will require careful consideration of experimental noise and imperfections. Despite these limitations, this work establishes a crucial theoretical foundation for achieving ultimate quantum precision in optical interferometry and opens new avenues for advanced quantum technologies.