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arXiv:2606.14254 · Optica

Dose-efficient Quantum Phase Estimation in Lossy Optical Interferometry

Qilin Yu, Ben Wang, Kaimin Zheng, Minghao Mi, Hui Li, Lijian Zhang

quant-phSubmitted Jun 12, 2026• Announced Jun 15, 2026• 0 citations
arXivHTMLPDF

Abstract

Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.

Journal reference
Optica 13, 1130-1136 (2026)
DOI
10.1364/OPTICA.595738

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Optical interferometry is a cornerstone technique for precise phase measurements across various fields. In many applications, for example, biological imaging, it often necessitates stringent limits on light intensity to prevent adverse effects on light-sensitive samples, a condition known as dose-limited regimes. Maximizing the precision per dose is therefore crucial. In quantum metrology, quantum correlations enable high precision in phase estimation while adhering to dose constraints. Nevertheless, photon loss, including absorption by a sample, substantially diminishes the benefits of quantum enhancement in interferometry. In this work, we experimentally investigate a dose-efficient approach to quantum phase estimation using sequential strategies in the presence of loss. Performance of sequential strategies with and without control is evaluated through quantum Fisher information (QFI) per dose. Experimental results show that both sequential strategies exceed the classical limit and outperform the parallel strategy using unbalanced N00N states. Notably, the control-enhanced sequential strategy attains superior QFI per dose, approaching the quantum limit. These results highlight the promise of sequential strategy for imaging and sensing in resource-constrained scenarios, marking a significant step toward practical and efficient quantum metrology in lossy environments.
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The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.
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Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cramer-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters, and has implications for sophisticated sensing scenarios such as quantum imaging.
This thesis presents a summary of the foundation and background of the field of quantum optics, and an analysis of some recent discoveries in various fields of which I have aided in furthering investigative research and advancement through publications. Such topics include numerical optimization of generalized quantum states used in phase sensitive quantum metrology, an analysis of object detection through the use of quantum interferometry in the presence of lossy conditions, and the use of the latter technique to propose an invisible quantum tripwire. First is a collaborative effort to numerically optimize quantum optical states for quantum metrological applications. We optimize two-mode, entangled, number states of light in the presence of loss in order to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss the optimal state is the so-called N00N state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss. The next topic is statistical hypothesis testing of interaction free measurement and a quantitative limit on the obtainable error. Previous analyses have been based solely on detection probabilities known only in the infinite photon limit. Our analysis assumes a finite number of photons, and an investigation of reliability in the presence of photon loss and phase fluctuations. We use symmetric hypothesis testing and the Chernoff bound to provide error estimation after N independent, single photon trials. Finally, we present a quantum optical interrogation technique capable of detecting an intrusion with very low probability of the quantum “tripwire” being revealed to the intruder. The tripwire exploits a curious nonlinear behavior of the quantum Zeno effect we discovered, which occurs in a lossy system. We also employ statistical hypothesis testing, allowing us to calculate a confidence level of interaction-free measurement after a given number of trials.
Abstract We propose a quantum-enhanced metrological scheme utilizing unbalanced entangled coherent states (ECSs) generated by passing a coherent state and a coherent state superposition through an unbalanced beam splitter (BS). We identify the optimal phase sensitivity of this scheme by maximizing the quantum Fisher information (QFI) with respect to the BS transmission ratio. Our scheme outperforms the conventional scheme with a balanced BS, particularly in the presence of single-mode photon loss. Notably, our scheme retains quantum advantage in phase sensitivity in the limit of high photon intensity, where the balanced scheme offers no advantage over the classical strategy.