Related papers: Generalized-mean Cram\'er-Rao Bounds for Multipara…
The theoretical foundation of quantum sensing is rooted in the Cram\'er-Rao formalism, which establishes quantitative precision bounds for a given quantum probe. In many practical scenarios, where more than one parameter is unknown, the…
Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…
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…
Quantum metrology enhances the sensitivity of parameter estimation using the distinctive resources of quantum mechanics such as entanglement. It has been shown that the precision of estimating an overall multiplicative factor of a…
We propose a modified $\chi^{\beta}$-divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cram\'er-Rao inequalities, involving this Fisher information,…
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 summarise important recent advances in quantum metrology, in connection to experiments in cold gases, trapped cold atoms and photons. First we review simple metrological setups, such as quantum metrology with spin squeezed states, with…
We derive several expressions for the quantum Fisher information matrix (QFIM) for the multi-parameter estimation of multi-mode Gaussian quantum states, the corresponding symmetric logarithmic derivatives, and conditions for saturability of…
The power of quantum sensing rests on its ultimate precision limit, quantified by the quantum Cramer-Rao bound (QCRB), which can surpass classical bounds. In multi-parameter estimation, the QCRB is not always saturated as the quantum nature…
Mixed-resolution architectures, combining high-resolution (analog) data with coarsely quantized (e.g., 1-bit) data, are widely employed in emerging communication and radar systems to reduce hardware costs and power consumption. However, the…
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…
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…
Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the…
The Bayesian Cram\'er-Rao bound (CRB) provides a lower bound on the mean square error of any Bayesian estimator under mild regularity conditions. It can be used to benchmark the performance of statistical estimators, and provides a…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
Neural networks are increasingly used to estimate parameters in quantitative MRI, in particular in magnetic resonance fingerprinting. Their advantages over the gold standard non-linear least square fitting are their superior speed and their…
In the present work, we show how the generalized Cram\'er-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on $\mathbb{R}^{n}$, and to a wider…
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…
In most quantum technologies, measurements need to be performed on the parametrized quantum states to transform the quantum information to classical information. The measurements, however, inevitably distort the information. The…