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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…
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…
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…
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…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…
Quantum metrology derives its capabilities from the careful employ of quantum resources for carrying out measurements. This advantage, however, relies on refined data postprocessing, assessed based on the variance of the estimated…
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…
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…
The laws of quantum mechanics allow to perform measurements whose precision supersedes results predicted by classical parameter estimation theory. That is, the precision bound imposed by the central limit theorem in the estimation of a…
A pivotal task in quantum metrology, and quantum parameter estimation in general, is to de- sign schemes that achieve the highest precision with given resources. Standard models of quantum metrology usually assume the dynamics is fixed, the…
A lower bound is an important tool for predicting the performance that an estimator can achieve under a particular statistical model. Bayesian bounds are a kind of such bounds which not only utilizes the observation statistics but also…
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,…
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…
The best possible precision is one of the key figures in metrology, but this is established by the exact response of the detection apparatus, which is often unknown. There exist techniques for detector characterisation, that have been…
A version of quantum Cram\'{e}r-Rao bound dictates that the covariance of any set of operators is bounded by a product of the derivatives of expectation values and the inverse of quantum metric. We elaborate that because quantum metric…
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…
This paper explores as didactically as possible the fundamental principles of both classical and quantum metrology, focusing on the Cram\'er-Rao Bound and how it defines the maximum precision in parameter estimation, taking into account…
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…
Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective 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…