Related papers: From quantum Bayesian inference to quantum tomogra…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
Conventional approximations to Bayesian inference rely on either approximations by statistics such as mean and covariance or by point particles. Recent advances such as the ensemble Gaussian mixture filter have generalized these notions to…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…
The possibility of reconciliation between canonical probability distributions obtained from the $q$-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
On the basis of statistical mechanics of the Q-Ising model, we formulate the Bayesian inference to the problem of inverse halftoning, which is the inverse process of representing gray-scales in images by means of black and white dots. Using…
This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. Inference is made tractable by…
We give several algorithms for reconstructing quantum states of swift electrons, using maximum likelihood estimation, Bayesian inversion, and deep learning. We apply these algorithms to data previously recorded for an attosecond electron…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
In this work a quantum analogue of Bayesian inference is considered. Based on the notion of instrument, we propose a quantum analogue of Bayes' rule, which elaborates how a prior normal state updates under observations. Besides, we…
In the operator formalism of quantum mechanics, the density operator describes the complete statistics of a quantum state in terms of d^2 independent elements, where d is the number of possible outcomes for a precise measurement of an…
In the field of signal processing, the sampling theorem plays a fundamental role for signal reconstruction as it bridges the gap between analog and digital signals. Following the celebrated Nyquist-Shannon sampling theorem, generalizing the…
We analyze general enough models of repeated indirect measurements in which a quantum system interacts repeatedly with randomly chosen probes on which Von Neumann direct measurements are performed. We prove, under suitable hypotheses, that…
Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…
Quantum state tomography, a process that reconstructs a quantum state from measurements on an ensemble of identically prepared copies, plays a crucial role in benchmarking quantum devices. However, brute-force approaches to quantum state…
We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…
We present a compressive quantum process tomography scheme that fully characterizes any rank-deficient completely-positive process with no a priori information about the process apart from the dimension of the system on which the process…
Two types of states are widely used in quantum mechanics, namely (deterministic-coefficient) pure states and statistical mixtures. A density operator can be associated with each of them. We here address a third type of states, that we…