Related papers: Comparison between the Cramer-Rao and the mini-max…
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as…
This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with…
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…
We present a general problem formulation for optimal parameter estimation based on quantized observations, with application to antenna array communication and processing (channel estimation, time-of-arrival (TOA) and direction-of-arrival…
We discuss a problem of parameter estimation for quantum two-level system, qubit system, in presence of unknown phase parameter. We analyze trade-off relations for mean-square errors when estimating relevant parameters with separable…
Bounding the optimal precision in parameter estimation tasks is of central importance for technological applications. In the regime of a small number of measurements, or that of low signal-to-noise ratios, the meaning of common frequentist…
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…
We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…
We calculate the quantum Cram\'er--Rao bound for the sensitivity with which one or several parameters, encoded in a general single-mode Gaussian state, can be estimated. This includes in particular the interesting case of mixed Gaussian…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
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…
This paper gives a replica analysis for the minimum mean square error (MSE) of a massive multiple-input multiple-output (MIMO) system by using Bayesian inference. The Bayes-optimal estimator is adopted to estimate the data symbols and the…
In this paper, we propose an oversampling based low-resolution aware least squares channel estimator for large-scale multiple-antenna systems with 1-bit analog-to-digital converters on each receive antenna. To mitigate the information loss…
In some estimation problems, not all the parameters can be identified, which results in singularity of the Fisher Information Matrix (FIM). The Cram\'er-Rao Bound (CRB), which is the inverse of the FIM, is then not defined. To regularize…
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…
We apply the formalism of quantum estimation theory to obtain information about the value of the nonlinear optomechanical coupling strength. In particular, we discuss the minimum mean-square error estimator and a quantum Cram\'er--Rao-type…
Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and…
Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the…
The design and analysis of diffusive molecular communication systems generally requires knowledge of the environment's physical and chemical properties. Furthermore, prospective applications might rely on the timely detection of changes in…
The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable…