Related papers: Local solutions of Maximum Likelihood Estimation i…
Maximum-likelihood estimation is applied to identification of an unknown quantum mechanical process represented by a ``black box''. In contrast to linear reconstruction schemes the proposed approach always yields physically sensible…
Precise reconstruction of unknown quantum states from measurement data, a process commonly called quantum state tomography, is a crucial component in the development of quantum information processing technologies. Many different tomography…
When performing maximum-likelihood quantum-state tomography, one must find the quantum state that maximizes the likelihood of the state given observed measurements on identically prepared systems. The optimization is usually performed with…
Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states…
Quantum mechanics predicts the existence of intrinsically random processes. Contrary to classical randomness, this lack of predictability can not be attributed to ignorance or lack of control. Here we find the optimal method to quantify the…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
The initialization of a quantum system into a certain state is a crucial aspect of quantum information science. While a variety of measurement strategies have been developed to characterize how well the system is initialized, for a given…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…
Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct with high fidelity,…
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…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
We show that the method of maximum likelihood (MML) provides us with an efficient scheme for reconstruction of quantum channels from incomplete measurement data. By construction this scheme always results in estimations of channels that are…
Recently we find several candidates of quantum algorithms that may be implementable in near-term devices for estimating the amplitude of a given quantum state, which is a core sub- routine in various computing tasks such as the Monte Carlo…
The Constrained Minimal Supersymmetric Standard Model (CMSSM) is one of the simplest and most widely-studied supersymmetric extensions to the standard model of particle physics. Nevertheless, current data do not sufficiently constrain the…
We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…
Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy…
In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best,…
Maximum likelihood estimation of a location parameter fails when the density have unbounded mode. An alternative approach is considered by leaving out a data point to avoid the unbounded density in the full likelihood. This modification…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…