Related papers: Valid lower bound for all estimators in quantum pa…
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…
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the…
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…
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that…
We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…
It is proved that in a non-Bayesian parametric estimation problem, if the Fisher information matrix (FIM) is singular, unbiased estimators for the unknown parameter will not exist. Cramer-Rao bound (CRB), a popular tool to lower bound the…
Determining when the multiparameter quantum Cram\'er--Rao bound (QCRB) is saturable with experimentally relevant single-copy measurements is a central open problem in quantum metrology. Here we establish an equivalence between QCRB…
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…
The Cram\'er-Rao bound (CRB), a well-known lower bound on the performance of any unbiased parameter estimator, has been used to study a wide variety of problems. However, to obtain the CRB, requires an analytical expression for the…
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…
In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse…
Sensing and imaging are among the most important applications of quantum information science. To investigate their fundamental limits and the possibility of quantum enhancements, researchers have for decades relied on the quantum…
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…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…
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…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…
This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…
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…
Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not…