Related papers: Quantum estimation for non-differentiable models
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…
We consider the problem of estimating a random state vector when there is information about the maximum distances between its subvectors. The estimation problem is posed in a Bayesian framework in which the minimum mean square error (MMSE)…
An optimal estimator of quantum states based on a modified Kalman Filter is presented in this work. Such estimator acts after state measurement, allowing to obtain an optimal estimation of quantum state resulting in the output of any…
We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the…
Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent…
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and…
We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…
Estimation of physical observables for unknown quantum states is an important problem that underlies a wide range of fields, including quantum information processing, quantum physics, and quantum chemistry. In the context of quantum…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
The simulation of electronic properties is a pivotal issue in modern electronic structure theory, driving significant efforts over the past decades to develop protocols for computing energy derivatives. In this work, we address this problem…
We establish a lower bound on the quantum coherence of an arbitrary quantum state in arbitrary dimension, using a noncommutativity estimator of an arbitrary observable of sub-unit norm, where the estimator is the commutator of the…
Quantum Metrology calculates the ultimate precision of all estimation strategies, measuring what is their root mean-square error (RMSE) and their Fisher information. Here, instead, we ask how many bits of the parameter we can recover,…
In this article we have suggested an improved estimator for estimating the population mean in simple random sampling using auxiliary information under the presence of measurement errors. The mean square error (MSE) of the proposed estimator…
The estimation of all the parameters in an unknown quantum state or measurement device, commonly known as quantum state tomography (QST) and quantum detector tomography (QDT), is crucial for comprehensively characterizing and controlling…
Extracting classical information from quantum systems is of fundamental importance, and classical shadows allow us to extract a large amount of information using relatively few measurements. Conventional shadow estimators are unbiased and…
Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE),…
We consider the problem of estimating the state of a large but finite number $N$ of identical quantum systems. In the limit of large $N$ the problem simplifies. In particular the only relevant measure of the quality of the estimation is the…
In this article we propose a method to estimate with high accuracy pure quantum states of a single qudit. Our method is based on the minimization of the squared error between the complex probability amplitudes of the unknown state and its…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer.…