Related papers: Fast state tomography with optimal error bounds
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography…
Quantum process tomography (QPT), used to estimate the linear map that best describes a quantum operation, is usually performed using a priori assumptions about state preparation and measurement (SPAM), which yield a biased and inconsistent…
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…
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,…
Point tomography is a new approach to the problem of state estimation, which is arguably the most efficient and simple method for modern high-precision quantum information experiments. In this scenario, the experimenter knows the target…
Partial Least Squares (PLS) is a widely used method for data integration, designed to extract latent components shared across paired high-dimensional datasets. Despite decades of practical success, a precise theoretical understanding of its…
In the paper the Bayesian and the least squares methods of quantum state tomography are compared for a single qubit. The quality of the estimates are compared by computer simulation when the true state is either mixed or pure. The fidelity…
With nowadays steadily growing quantum processors, it is required to develop new quantum tomography tools that are tailored for high-dimensional systems. In this work, we describe such a computational tool, based on recent ideas from…
In this paper, the problem of robust estimation and validation of location-scale families is revisited. The proposed methods exploit the joint asymptotic normality of sample quantiles (of i.i.d random variables) to construct the ordinary…
Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer…
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose…
Quantum state tomography (QST), the task of estimating an unknown quantum state given measurement outcomes, is essential to building reliable quantum computing devices. Whereas computing the maximum-likelihood (ML) estimate corresponds to…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
Quantum state and process tomography are typically analyzed under the assumption that devices emit independent and identically distributed (i.i.d.) states or channels. In realistic experiments, however, noise, drift, feedback, or…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
Instead of minimizing the sum of all $n$ squared residuals as the classical least squares (LS) does, Rousseeuw (1984) proposed to minimize the sum of $h$ ($n/2 \leq h < n$) smallest squared residuals, the resulting estimator is called least…
In this paper we propose a new approach to study the properties of the Partial Least Squares (PLS) estimator. This approach relies on the link between PLS and discrete orthogonal polynomials. Indeed many important PLS objects can be…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…