相关论文: Maximum-likelihood method in quantum estimation

Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce 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…

Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial…

One of the main quests in quantum metrology, and quantum parameter estimation in general, is to find out the highest achievable precision with given resources and design schemes that attain that precision. In this article we present a…

We extend the concept of probabilistic unambiguous discrimination of quantum states to quantum state estimation. We consider a scenario where the measurement device can output either an estimate of the unknown input state or an inconclusive…

We propose an iterative algorithm for incomplete quantum process tomography, with the help of quantum state estimation, based on the combined principles of maximum-likelihood and maximum-entropy. The algorithm yields a unique estimator for…

The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…

We study the optimization of any quantum process by minimizing the "randomness" in the measurement result at the output of that quantum process. We conceptualize and propose a measure of such randomness and inquire whether an optimization…

In this work, we consider the problem of online (real-time, single-shot) estimation of static or slow-varying parameters along quantum trajectories in quantum dynamical systems. Based on the measurement signal of a continuously-monitored…

We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…

There exists, in general, a convex set of quantum state estimators that maximize the likelihood for informationally incomplete data. We propose an estimation scheme, catered to measurement data of this kind, to search for the exact…

We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…

Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…

The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it…

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of…

We propose a novel molecular computing scheme for statistical inference. We focus on the much-studied statistical inference problem of computing maximum likelihood estimators for log-linear models. Our scheme takes log-linear models to…

(Neal and Hinton, 1998) recast maximum likelihood estimation of any given latent variable model as the minimization of a free energy functional $F$, and the EM algorithm as coordinate descent applied to $F$. Here, we explore alternative…

Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of…

Maximum likelihood method is widely used for parameter estimation in high energy physics. To consider various systematic uncertainties, tens of or even hundreds of nuisance parameters (NP) are introduced in a likelihood fit. The constraint…