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The quantum Cram\'er-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a…

Quantum Physics · Physics 2021-09-15 Aaron Z. Goldberg , Luis L. Sánchez-Soto , Hugo Ferretti

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…

A fundamental challenge in multiparameter quantum estimation arises from the incompatibility of optimal measurements for different parameters, leading to intricate precision trade-offs that obscure the understanding of ultimate quantum…

Quantum Physics · Physics 2026-05-25 Lingna Wang , Hongzhen Chen , Haidong Yuan

Quantum multiparameter estimation focuses on the simultaneous inference of multiple parameters in quantum systems through measurement and data processing. Its complexity stems from two key factors: measurement incompatibility and parameter…

Quantum Physics · Physics 2025-09-15 Bing-Shu Hu , Xiao-Ming Lu

We show that the quantum Cram\'er-Rao bound on the precision of measurements of the optical phase gradient, or the wavefront tilt, with a beam of finite width is consistent with the Heisenberg uncertainty principle for a single-photon…

Quantum Physics · Physics 2020-07-22 Walker Larson , Bahaa E. A. Saleh

The quantum Cram\'er-Rao bound for the joint estimation of the centroid and the separation between two incoherent point sources cannot be saturated. As such, the optimal measurements for extracting maximal information about both at the same…

Quantum Physics · Physics 2025-03-21 J. Řeháček , J. L. Romero , A. Z. Goldberg , Z. Hradil , L. L. Sánchez-Soto

We present a novel strategy for obtaining optimal probe states and measurement schemes in a class of noiseless multiparameter estimation problems with symmetry among the generators. The key to the framework is the introduction of a set of…

Quantum Physics · Physics 2024-09-26 Sivaprasad Omanakuttan , Jonathan A. Gross , T. J. Volkoff

Given a finite number $N$ of copies of a qubit state we compute the maximum fidelity that can be attained using joint-measurement protocols for estimating its purity. We prove that in the asymptotic $N\to\infty$ limit, separable-measurement…

Quantum Physics · Physics 2009-11-11 E. Bagan , M. A. Ballester , R. Munoz-Tapia , O. Romero-Isart

We generalize the approach by Braunstein and Caves [Phys. Rev. Lett. 72, 3439 (1994)] to quantum multi-parameter estimation with general states. We derive a matrix bound of the classical Fisher information matrix due to each measurement…

Quantum Physics · Physics 2019-09-10 Jing Yang , Shengshi Pang , Yiyu Zhou , Andrew N. Jordan

Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…

Quantum Physics · Physics 2020-03-16 Ilya Kull , Philippe Allard Guérin , Frank Verstraete

Estimation of physical parameters encoded in a Hamiltonian is a central task in quantum sensing and learning. While the ultimate precision limit for estimating a single parameter coupled to a single generator is well established, the…

We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for…

Quantum Physics · Physics 2013-05-29 Kevin C. Young , Mohan Sarovar , Robert Kosut , K. Birgitta Whaley

Simultaneous estimation of multiple parameters in quantum metrological models is complicated by factors relating to the (i) existence of a single probe state allowing for optimal sensitivity for all parameters of interest, (ii) existence of…

Quantum Physics · Physics 2019-02-01 Sammy Ragy , Marcin Jarzyna , Rafal Demkowicz-Dobrzanski

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

We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation…

Quantum Physics · Physics 2019-04-23 Haijun Xing , Libin Fu , Su Yi

Quantum metrology aims to enhance measurement precision beyond the classical limit by leveraging quantum resources. Unlike multi-parameter dynamic quantum metrology, many questions regarding multiparameter quantum metrology at thermal…

Quantum Physics · Physics 2026-05-20 Zhu Cao

Relativistic quantum metrology provides an optimal strategy for the estimation of parameters encoded in quantum fields in flat and curved spacetime. These parameters usually correspond to physical quantities of interest such as proper…

Quantum Physics · Physics 2017-05-25 Dominik Šafránek , Jan Kohlrus , David Edward Bruschi , Antony R. Lee , Ivette Fuentes

Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…

Quantum Physics · Physics 2015-05-01 Takanori Sugiyama

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…

Quantum Physics · Physics 2017-02-08 Olivier Pinel , Pu Jian , Claude Fabre , Nicolas Treps , Daniel Braun

We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…

Quantum Physics · Physics 2015-06-16 O. Pinel , P. Jian , N. Treps , C. Fabre , and D. Braun