Quantum Metrology Achieves Precision Beyond Limits with Just 2 Measurement Bins

Scientists are continually striving to enhance measurement precision beyond conventional boundaries, but quantum metrology is frequently hampered by real-world experimental flaws. Byeong-Yoon Go, Geunhee Gwak (from the Korea Advanced Institute of Science and Technology), Young-Do Yoon, and colleagues , including Sungho Lee, Nicolas Treps, and Jiyong Park , have now investigated how ‘coarse-graining’ during measurement impacts quantum precision. Their theoretical and experimental work, detailed in this paper, reveals that even severely limited measurements , using as few as two data points , can still surpass classical limits and approach the ultimate Heisenberg scaling for phase estimation. This discovery offers a significant and practical route towards achieving quantum enhancement despite substantial experimental imperfections, potentially broadening the applicability of quantum technologies.

Coarse graining’s impact on squeezed light precision

Scientists have demonstrated a pathway to maintain quantum enhancement in measurement precision even when faced with significant experimental imperfections, specifically addressing the issue of coarse graining in quantum measurement. The research, published on January 23, 2026, details both theoretical analysis and experimental verification of how discretizing measurement outcomes, a process known as coarse graining, impacts the precision of phase estimation using squeezed light. The team employed an interferometer utilising a squeezed vacuum and a laser input to meticulously analyse the effects of coarse graining on homodyne detection, a standard technique in quantum metrology.
They evaluated the Fisher information, a key metric for determining the ultimate limit of estimation precision, under various coarse-graining conditions, and crucially, devised an optimal estimation strategy that achieves the Cramér-Rao bound, representing the best possible precision attainable. Remarkably, even with extremely coarse measurement, using only two discrete bins, the study reveals that phase estimation can surpass the standard quantum limit and approach the Heisenberg scaling, a regime of enhanced precision. This finding challenges the conventional wisdom that experimental imperfections inevitably degrade quantum performance. Experiments show a 1.2 dB enhancement in phase estimation using only two bins compared to classical methods employing ideal measurement, with performance improving to 3.8 dB as the number of bins increases.

To achieve this, the researchers employed the method of moments, developing calibration procedures applicable to a wide range of experimental setups. This innovative approach allows for the determination of optimal weights for combining observables from the coarse-grained measurement, effectively mitigating the loss of information caused by discretization. The work establishes a practical route to achieving quantum enhancement despite the presence of severe experimental limitations, opening new avenues for the development of robust quantum sensors. This breakthrough reveals that coarse graining, often considered a detrimental effect, can be overcome with intelligent data analysis and calibration.

The study unveils a method to extract maximum information from even highly discretized measurements, preserving the benefits of quantum enhancement. By focusing on the imperfections inherent in the measurement process itself, the research offers a significant contribution to the field of quantum metrology and has implications for a broad range of applications, including gravitational wave detection, optomechanical sensing, and high-precision imaging. The team’s findings suggest that practical quantum sensors can be designed and implemented even in the presence of substantial experimental challenges, paving the way for more accessible and reliable quantum technologies.

Coarse Graining’s Impact on Phase Estimation is significant

0.2 dB enhancement in quantum estimation using only two bins compared to classical methods utilising ideal measurement, with performance improving towards 3.8 dB as the number of bins increased. This substantial improvement highlights a viable pathway towards achieving quantum enhancement even when confronted with significant experimental imperfections. The experimental. Experiments revealed that even with extremely coarse-grained measurement, utilising only two bins, phase estimation can surpass classical limits and approach Heisenberg scaling, a significant advancement in measurement sensitivity.

This work highlights a practical pathway to maintaining quantum enhancement despite realistic experimental limitations. The team measured the Fisher information under various coarse-graining conditions, meticulously determining an optimal estimation strategy that saturates the Cramér-Rao bound. Remarkably, even when employing only two bins for data collection, the study observed a quantum enhancement of 1.2 dB compared to classical methods utilising ideal measurements. This enhancement progressively improved towards 3.8 dB as the number of bins increased, demonstrating a clear correlation between measurement resolution and performance.

These results confirm that coarse graining, traditionally considered a detrimental effect, can be mitigated through optimised data analysis techniques. Experiments involved an interferometer with a squeezed vacuum and a laser input, allowing researchers to analyse how discretisation in homodyne detection affects phase estimation precision. Data shows that coarse-grained measurement retains a substantial fraction, 64% with just two bins, of the Fisher information achievable with ideal, fine-grained measurements. This retention of information is crucial, as it not only enables quantum-enhanced phase estimation but also supports the possibility of achieving Heisenberg scaling, a regime where precision increases inversely with the number of particles measured.

To determine the optimal estimation strategy, scientists employed the method of moments and developed calibration procedures applicable to general experimental settings. The breakthrough delivers a practical solution for enhancing quantum metrology in the presence of significant experimental imperfections, opening doors for improved sensing applications. Tests prove that by formulating multiple observables corresponding to each bin in the coarse-grained measurement, the team derived optimal weights for their linear combination, effectively saturating the Cramér-Rao bound and maximising precision. This calibration process, directly applied to the experiment, allowed for precise phase estimation even with limited data resolution.

Coarse Graining Still Enables Heisenberg Scaling despite decoherence

Scientists have demonstrated a strategy for quantum-enhanced phase estimation even when faced with coarse graining, a common imperfection in quantum measurements that reduces resolution. Their work centres on analysing how this coarse graining affects the precision of phase estimation in homodyne detection, utilising both theoretical analysis and experimental verification with squeezed vacuum and laser inputs. Remarkably, the researchers found that even with extremely coarse measurements, using only two bins, phase estimation can surpass the standard quantum limit and approach Heisenberg scaling. The study establishes that coarse-grained measurement can retain a substantial portion of the Fisher information achievable with ideal measurement, enabling quantum enhancement and even Heisenberg-limited phase estimation.

To fully exploit this capability, the team developed a method to determine an optimal observable for phase estimation, effectively saturating the Cramér-Rao bound. In a proof-of-principle experiment employing 3.8 dB of squeezed vacuum, they observed a quantum enhancement of 1.2 dB with a two-bin measurement, improving towards 3.8 dB as the number of bins increased. The authors acknowledge that the technique’s effectiveness is particularly crucial as squeezing levels and homodyne detection ranges expand, and that the current analysis assumes Gaussian states. These findings are significant as they offer a practical pathway to achieving quantum enhancement despite substantial experimental imperfections, broadening the scope of quantum metrology. Future research could extend this approach to other continuous-variable quantum measurements, such as quantum imaging and quantum spectroscopy, potentially enhancing sensitivity in a variety of sensing applications. This work therefore provides a valuable method for realising quantum metrology in realistic experimental conditions.