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Precise estimation of physical parameters underpins both scientific discovery and technological development. A central goal of quantum metrology and sensing is to exploit quantum resources like entanglement to devise optimal strategies for…
We analyse the precision limits for simultaneous estimation of a pair of conjugate parameters in a displacement channel using Gaussian probes. Having a set of squeezed states as an initial resource, we compute the Holevo Cram\'er-Rao bound…
The optimal quantum measurements for estimating different unknown parameters in a parameterized quantum state are usually incompatible with each other. Traditional approaches to addressing the measurement incompatibility issue, such as the…
We present a comprehensive and pedagogical formulation of Bayesian multiparameter quantum estimation. Within this framework, we analyse the role of measurement incompatibility and establish its quantitative effect on attainable precision.…
Multiparameter quantum estimation faces a fundamental challenge due to the inherent incompatibility of optimal measurements for different parameters, a direct consequence of quantum non-commutativity. This incompatibility is quantified by…
High-precision sensors that exploit uniquely quantum phenomena have been shown to surpass the standard quantum limit of measurement precision. However, in the general scenario where multiple parameters are simultaneously encoded in a…
In quantum metrology, the Holevo Cram\'er-Rao bound has attracted renewed interest in recent years due to its superiority over the Helstrom Cram\'er-Rao bound and its asymptotic attainability for multi-parameter estimation. Its evaluation,…
We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is…
Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of…
We discuss the ultimate precision bounds on the multiparameter estimation of single- and two-mode pure Gaussian states. By leveraging on previous approaches that focused on the estimation of a complex displacement only, we derive the Holevo…
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…
How well can multiple incompatible observables be implemented by a single measurement? This is a fundamental problem in quantum mechanics with wide implications for the performance optimization of numerous tasks in quantum information…
We study quantum-limited 3D magnetometry using two qubits. Two qubits form the smallest multi-qubit system for 3D magnetometry, the simultaneous estimation of three phases, as it is impossible with a single qubit. We provide an analytical…
We discuss the Heisenberg limit in the multiparameter metrology within two different paradigms -- the one, where the measurement is repeated many times (so the Cram\'er-Rao bound is guaranteed to be asymptotically saturable) and the second…
Quantum parameter estimation theory is an important component of quantum information theory and provides the statistical foundation that underpins important topics such as quantum system identification and quantum waveform estimation. When…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
We derive an asymptotic lower bound on the Bayes risk when N identical quantum systems whose state depends on a vector of unknown parameters are jointly measured in an arbitrary way and the parameters of interest estimated on the basis of…
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…
Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…
The aim of the channel estimation is to estimate the parameters encoded in a quantum channel. For this aim, it is allowed to choose the input state as well as the measurement to get the outcome. Various precision bounds are known for the…