相关论文: Optimal, reliable estimation of quantum states

The accurate estimation of observables is a crucial task in quantum computing. Recent advances have highlighted the need for (a) specialized protocols for qudit-based devices, that include (b) error-aware strategies. Here, we present…

Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…

In applications of Bayesian procedures, once a class of priors has been chosen, it may be tempting to fix the prior's hyperparameters from the data, in an empirical Bayes (EB) fashion, usually by their maximum marginal likelihood estimates…

Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…

The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…

A longstanding problem in quantum metrology is how to extract as much information as possible in realistic scenarios with not only multiple unknown parameters, but also limited measurement data and some degree of prior information. Here we…

Robust decision making involves making decisions in the presence of uncertainty and is often used in critical domains such as healthcare, supply chains, and finance. Causality plays a crucial role in decision-making as it predicts the…

We compare the accuracy, precision and reliability of different methods for estimating key system parameters for two-level systems subject to Hamiltonian evolution and decoherence. It is demonstrated that the use of Bayesian modelling and…

We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with nonparametric prior for the random intercepts, slopes, dynamics, and non-spherical error variances. We establish identification and consistency of…

Quantum detectors provide information about quantum systems by establishing correlations between certain properties of those systems and a set of macroscopically distinct states of the corresponding measurement devices. A natural question…

We report our theoretical and experimental investigations into errors in quantum state estimation, putting a special emphasis on their asymptotic behavior. Tomographic measurements and maximum likelihood estimation are used for estimating…

Quantum state smoothing is a technique to estimate an unknown true state of an open quantum system based on partial measurement information both prior and posterior to the time of interest. In this paper, we show that the smoothed quantum…

Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…

It is proposed in the literature that in some complicated problems maximum likelihood estimates (MLE) are not suitable or even do not exist. An alternative to MLE for estimation of the parameters is the Bayesian method. The Markov chain…

A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…

Quantum phase estimation (QPE) is a cornerstone algorithm for extracting Hamiltonian eigenvalues, but its standard, eigenstate-centric form relies on carefully prepared coherent inputs that are costly or impractical for many strongly…

We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with i.i.d. normal errors. We prove that under mild moment conditions on the unknown means, the average mean…

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 Expectation-Maximization (EM) algorithm is a commonly used method for finding the maximum likelihood estimates of the parameters in a mixture model via coordinate ascent. A serious pitfall with the algorithm is that in the case of…

In this paper, we focus on alternate forms of the T-matrix used in the Maximum Likelihood Estimate (MLE) procedure for fitting the experimental data collected in quantum state tomography experiments. In particular, we analyze the single…