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The measured relative entropies of quantum states and channels find operational significance in quantum information theory as achievable error rates in hypothesis testing tasks. They are of interest in the near term, as they correspond to…
Traditional measures of entropy, like the Von Neumann entropy, while fundamental in quantum information theory, are insufficient when interpreted as thermodynamic entropy due to their invariance under unitary transformations, which…
The inefficiency of using an unbiased estimator in a Monte Carlo procedure can be quantified using an inefficiency constant, equal to the product of the variance of the estimator and its mean computational cost. We develop methods for…
The entropic uncertainty relation with quantum side information (EUR-QSI) from [Berta et al., Nat. Phys. 6, 659 (2010)] is a unifying principle relating two distinctive features of quantum mechanics: quantum uncertainty due to measurement…
We study an entropy measure for quantum systems that generalizes the von Neumann entropy as well as its classical counterpart, the Gibbs or Shannon entropy. The entropy measure is based on hypothesis testing and has an elegant formulation…
We introduce a novel generalization of entropy and conditional entropy from which most definitions from the literature can be derived as particular cases. Within this general framework, we investigate the problem of designing…
The heteroscedastic probabilistic principal component analysis (PCA) technique, a variant of the classic PCA that considers data heterogeneity, is receiving more and more attention in the data science and signal processing communities. In…
Problems of probabilistic inference and decision making under uncertainty commonly involve continuous random variables. Often these are discretized to a few points, to simplify assessments and computations. An alternative approximation is…
A lower bound on the R\'enyi differential entropy of a sum of independent random vectors is demonstrated in terms of rearrangements. For the special case of Boltzmann-Shannon entropy, this lower bound is better than that given by the…
Researchers in physical science aim to uncover universal features in strongly interacting many-body systems, often hidden in complicated observables like entanglement entropy (EE). The non-local nature of EE makes it challenging to compute…
Entropic uncertainty relations are interesting in their own rights as well as for a lot of applications. Keeping this in mind, we try to make the corresponding inequalities as tight as possible. The use of parametrized entropies also allows…
We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…
The recent introduction of geometric partition entropy brought a new viewpoint to non-parametric entropy quantification that incorporated the impacts of informative outliers, but its original formulation was limited to the context of a…
We derive mean-field information Hessian matrices on finite graphs. The "information" refers to entropy functions on the probability simplex. And the "mean-field" means nonlinear weight functions of probabilities supported on graphs. These…
In this paper, we present a novel method for computing the relative entropy as well as the expected relative entropy using an MCMC chain. The relative entropy from information theory can be used to quantify differences in posterior…
The most natural way to describe an information-carrying system containing a specific noise is an additive white Gaussian-noise (AWGN) channel. In bosonic quantum systems (especially the Gaussian case), although the classical information…
For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…
Power iteration has been generalized to solve many interesting problems in machine learning and statistics. Despite its striking success, theoretical understanding of when and how such an algorithm enjoys good convergence property is…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…
In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredients, we derive an explicit and simple formula for the…