Related papers: Local solutions of Maximum Likelihood Estimation i…
In this work, we propose a machine learning-based approach to address a specific aspect of the Quantum Marginal Problem: reconstructing a global density matrix compatible with a given set of quantum marginals. Our method integrates a…
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or…
We describe quantum tomography as an inverse statistical problem and show how entropy methods can be used to study the behaviour of sieved maximum likelihood estimators. There remain many open problems, and a main purpose of the paper is to…
Quantum entanglement is an indispensable resource for many significant quantum information processing tasks. Thus, distilling more entanglement from less entangled resource is a task of practical significance and has been investigated for…
Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
We derive the optimal measurement for quantum state discrimination without a priori probabilities, i.e. in a minimax strategy instead of the usually considered Bayesian one. We consider both minimal-error and unambiguous discrimination…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem…
In this paper, we will discuss how to generalize nonparametric density estimators to MLE parametric estimators. Basing on the Parzen window theory and using the advantages of probability amplitude of quantum theory, we model a nonlinear…
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a…
Quantum computation has been growing rapidly in both theory and experiments. In particular, quantum computing devices with a large number of qubits have been developed by IBM, Google, IonQ, and others. The current quantum computing devices…
The local purity of large many-body quantum systems can be studied by following a statistical mechanical approach based on a random matrix model. Restricting the analysis to the case of global pure states, this method proved to be…
In this paper, we consider a novel and robust maximum likelihood approach to localizing radiation sources with unknown statistics of the source signal strength. The result utilizes the smallest number of sensors required theoretically to…
We consider parameter estimation in finite hidden state space Markov models with time-dependent inhomogeneous noise, where the inhomogeneity vanishes sufficiently fast. Based on the concept of asymptotic mean stationary processes we prove…
Quantum state tomography (QST) remains the gold standard for benchmarking and verification of near-term quantum devices. While QST for a generic quantum many-body state requires an exponentially large amount of resources, most physical…
Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
A novel computational approach to log-concave density estimation is proposed. Previous approaches utilize the piecewise-affine parametrization of the density induced by the given sample set. The number of parameters as well as non-smooth…