Related papers: Quantum Cram\'er-Rao bound for quantum statistical…
We address the discontinuities of the quantum Fisher information (QFI) that may arise when the parameter of interest takes values that change the rank of the quantum statistical model. We revisit the classical and the quantum Cram\'er-Rao…
The quantum Cram\'er-Rao bound sets a fundamental limit on the accuracy of unbiased parameter estimation in quantum systems, relating the uncertainty in determining a parameter to the inverse of the quantum Fisher information. We…
The quantum Fisher information constrains the achievable precision in parameter estimation via the quantum Cram\'er-Rao bound, which has attracted much attention in Hermitian systems since the 60s of the last century. However, less…
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…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory the variance of an unbiased parameter estimator is bounded from below by the inverse of…
The Cramer-Rao bound, satisfied by classical Fisher information, a key quantity in information theory, has been shown in different contexts to give rise to the Heisenberg uncertainty principle of quantum mechanics. In this paper, we show…
Many results in the quantum metrology literature use the Cram\'er-Rao bound and the Fisher information to compare different quantum estimation strategies. However, there are several assumptions that go into the construction of these tools,…
In multiparameter quantum metrology, the weighted-arithmetic-mean error of estimation is often used as a scalar cost function to be minimized during design optimization. However, other types of mean error can reveal different facets of…
In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cram\'{e}r-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision…
Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…
We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe. We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a…
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…
The quantum Cram\'er-Rao theorem states that the quantum Fisher information (QFI) bounds the best achievable precision in the estimation of a quantum parameter $\xi$. This is true, however, under the assumption that the measurement employed…
As we enter the era of quantum technologies, quantum estimation theory provides an operationally motivating framework for determining high precision devices in modern technological applications. The aim of any estimation process is to…
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed…
The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We study the task of estimating unknown parameters encoded in a channel in the sequential setting. A sequential strategy is the…
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the…
We provide a new expression of the quantum Fisher information(QFI) for a general system. Utilizing this expression, the QFI for a non-full rank density matrix is only determined by its support. This expression can bring convenience for a…
The attainability of the quantum Cram\'er-Rao bound [QCR], the ultimate limit in the precision of the estimation of a physical parameter, requires the saturation of the quantum information bound [QIB]. This occurs when the Fisher…