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Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial…

Optics · Physics 2015-09-04 Chien-Hung Lu , Matthew Reichert , Xiaohang Sun , Jason W. Fleischer

In multi-parameter quantum metrology, the resource of entanglement can lead to an increase in efficiency of the estimation process. Entanglement can be used in the state preparation stage, or the measurement stage, or both, to harness this…

Quantum Physics · Physics 2025-10-01 Aritra Das , Lorcán O. Conlon , Jun Suzuki , Simon K. Yung , Ping K. Lam , Syed M. Assad

This is a tutorial aimed at illustrating some recent developments in quantum parameter estimation beyond the Cram\`er-Rao bound, as well as their applications in quantum metrology. Our starting point is the observation that there are…

Quantum Physics · Physics 2020-03-06 Luigi Seveso , Matteo G. A. Paris

Shaping single-mode operation in high-power fibres requires a precise knowledge of the gain-medium optical properties. This requires accurate measurements of the refractive index differences ($\Delta$n) between the core and the cladding of…

Distributed quantum sensing exploits entanglement to enhance the estimation of multiple parameters across a network of spatially-separated sensors, achieving sensitivities beyond the classical limit. Potential applications cover a plethora…

Quantum interferometry methods exploit quantum resources, such as photonic entanglement, to enhance phase estimation beyond classical limits. Nonlinear optics has served as a workhorse for the generation of entangled photon pairs, ensuring…

Quantum Physics · Physics 2025-08-04 Romain Dalidet , Anthony Martin , Grégory Sauder , Laurent Labonté , Sébastien Tanzilli

Quantum-enhanced metrology can be achieved by entangling a probe with an auxiliary system, passing the probe through an interferometer, and subsequently making measurements on both the probe and auxiliary system. Conceptually, this…

Quantum Physics · Physics 2015-09-22 Simon A. Haine , Stuart S. Szigeti

A usual assumption in quantum estimation is that the unknown parameter labels the possible states of the system, while it influences neither the sample space of outcomes nor the measurement aimed at extracting information on the parameter…

Quantum Physics · Physics 2017-01-18 Luigi Seveso , Matteo A. C. Rossi , Matteo G. A. Paris

Nonlinear interactions are recognized as potential resources for quantum metrology, facilitating parameter estimation precisions that scale as the exponential Heisenberg limit of $2^{-N}$. We explore such nonlinearity and propose an…

Quantum-correlated interferometer is a newly emerging tool in quantum technology that offers classical-limit-breaking phase sensitivity. But to date, there exists a configurational bottleneck for its practicability due to the low…

Atomic Physics · Physics 2025-01-10 Wei Du , Shuhe Wu , Dong Zhang , Jun Chen , Yiquan Yang , Peiyu Yang , Jinxian Guo , Guzhi Bao , Weiping Zhang

The Cram\'er-Rao bound captures completely the performance of single-parameter quantum sensors. On the other hand, its extension to multiple parameters demands more caution. Different aspects need to be captured at once, including,…

Quantum Physics · Physics 2026-01-14 Jayanth Jayakumar , Marco Barbieri , Magdalena Stobińska

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical…

Quantum metrology allows for a huge boost in the precision of parameters estimation. However, it seems to be extremely sensitive on the noise. Bound entangled states are states with large amount of noise what makes them unusable for almost…

Quantum Physics · Physics 2015-12-09 L. Czekaj , A. Przysiezna , M. Horodecki , P. Horodecki

Entanglement is a fundamental resource that allows quantum sensors to surpass the standard quantum limit set by the quantum collapse of independent atoms. Collective cavity-QED systems have succeeded in generating large amounts of directly…

Quantum Physics · Physics 2023-03-30 Graham P. Greve , Chengyi Luo , Baochen Wu , James K. Thompson

The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…

Quantum Physics · Physics 2024-11-25 Ben Wang , Kaimin Zheng , Qian Xie , Aonan Zhang , Liang Xu , Lijian Zhang

Breaking the standard quantum limit in the sensing of parameters at different spatial locations, such as in a quantum network, is of great importance. Using the framework of quantum Fisher information, many strategies based on squeezed…

Quantum Physics · Physics 2025-10-01 Girish S. Agarwal

In quantum metrology, one of the major applications of quantum technologies, the ultimate precision of estimating an unknown parameter is often stated in terms of the Cram\'er-Rao bound. Yet, the latter is no longer guaranteed to carry an…

Classical measurement strategies in many areas are approaching their maximum resolution and sensitivity levels, but these levels often still fall far short of the ultimate limits allowed by the laws of physics. To go further, strategies…

Quantum Physics · Physics 2015-12-09 David S. Simon

We obtain the ultimate quantum limit for estimating the transverse separation of two thermal point sources using a given imaging system with limited spatial bandwidth. We show via the quantum Cram\'er-Rao bound that, contrary to the…

Quantum Physics · Physics 2016-11-29 Ranjith Nair , Mankei Tsang

Quantum entanglement is one of the core features of quantum theory. While it is typically revealed by measurements along carefully chosen directions, here we review different methods based on so-called random or randomized measurements.…

Quantum Physics · Physics 2020-11-24 Lukas Knips