Related papers: Comparative Noninformativities of Quantum Priors B…
The two principal/immediate influences -- which we seek to interrelate here -- upon the undertaking of this study are papers of Zyczkowski and Slomczy\'nski (J. Phys. A 34, 6689 [2001]) and of Petz and Sudar (J. Math. Phys. 37, 2262…
Integral representations of quantum relative entropy, and of the directional second and higher order derivatives of von Neumann entropy, are established, and used to give simple proofs of fundamental, known data processing inequalities: the…
The uncertainty principle restricts potential information one gains about physical properties of the measured particle. However, if the particle is prepared in entanglement with a quantum memory, the corresponding entropic uncertainty…
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…
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…
The random matrix ensembles (RME) of quantum statistical Hamiltonians, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied in literature to following quantum statistical systems:…
Uncertainty principle is a striking and fundamental feature in quantum mechanics distinguishing from classical mechanics. It offers an important lower bound to predict outcomes of two arbitrary incompatible observables measured on a…
We consider finite-dimensional linear Gaussian Bayesian inverse problems with uncorrelated sensor measurements. In this setting, it is known that the expected information gain, quantified by the expected Kullback-Leibler divergence from the…
Information metrics give lower bounds for the estimation of parameters. The Cencov-Morozova-Petz Theorem classifies the monotone quantum Fisher metrics. The optimum bound for the quantum estimation problem is offered by the metric which is…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states.…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
Elliptical distribution is a basic assumption underlying many multivariate statistical methods. For example, in sufficient dimension reduction and statistical graphical models, this assumption is routinely imposed to simplify the data…
We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…
The current study aims to examine uncertainty relations for measurements from generalized equiangular tight frames. Informationally overcomplete measurements are a valuable tool in quantum information processing, including tomography and…
Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…
We pedagogically present the information theory as originally established, explaining its essential ideas and paying attention to the expression employed to measure the amount of information. Also we discussed relationships between…