Related papers: Estimates for compression norms and additivity vio…

This paper proposes two estimators of the joint entropy of the Type-II censored data. Consistency of both estimators is proved. Simulation results show that the second one shows less bias and root of mean square error (RMSE) than leading…

Machine learning models must continuously self-adjust themselves for novel data distribution in the open world. As the predominant principle, entropy minimization (EM) has been proven to be a simple yet effective cornerstone in existing…

Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…

We introduce and apply Hilbert's projective metric in the context of quantum information theory. The metric is induced by convex cones such as the sets of positive, separable or PPT operators. It provides bounds on measures for statistical…

The deterministic notions of capacity and entropy are studied in the context of communication and storage of information using square-integrable, bandlimited signals subject to perturbation. The $(\epsilon,\delta)$-capacity, that extends…

Using the brick wall regularization of 't Hooft, the entropy of non-extreme and extreme black holes is investigated in a general static, spherically symmetric spacetime. We classify the singularity in the entropy by introducing a {\it new}…

This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…

We study the additivity problems for the classical capacity of quantum channels, the minimal output entropy and its convex closure. We show for each of them that additivity for arbitrary pairs of channels holds iff it holds for arbitrary…

Randomness extraction against side information is the art of distilling from a given source a key which is almost uniform conditioned on the side information. This paper provides randomness extraction against quantum side information whose…

We investigate how to measure and define the entropy of a simple chaotic system, three hard spheres on a ring. A novel approach is presented, which does not assume the ergodic hypothesis. It consists of transforming the particles collision…

We introduce the Clifford entropy, a measure of how close an arbitrary unitary is to a Clifford unitary, which generalizes the stabilizer entropy for states. We show that this quantity vanishes if and only if a unitary is Clifford, is…

We suggest a tight inequality for norms in $d$-dimensional space $l_p $ which has simple formulation but appears hard to prove. We give a proof for $d=3$ and provide a detailed numerical check for $d\leq 200$ confirming the conjecture. We…

We revisit generalized entropic formulations of the uncertainty principle for an arbitrary pair of quantum observables in two-dimensional Hilbert space. R\'enyi entropy is used as uncertainty measure associated with the distribution…

We consider the problem of approximating the empirical Shannon entropy of a high-frequency data stream under the relaxed strict-turnstile model, when space limitations make exact computation infeasible. An equivalent measure of entropy is…

A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…

We deal with the problem of the adaptive estimation of the $\mathbb{L}_2$-norm of a probability density on $\mathbb{R}^d$, $d\geq 1$, from independent observations. The unknown density is assumed to be uniformly bounded and to belong to the…

We consider the statistical problem of `compressive' estimation of low rank states with random basis measurements, where the estimation error is expressed terms of two metrics - the Frobenius norm and quantum infidelity. It is known that…

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…

We study the problem of generating a random variate $X$ from a finite discrete probability distribution $P$ using an entropy source of independent fair coin flips. A classic result from Knuth and Yao shows that the optimal expected number…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible constrained to match empirical data, for instance, feature expectations. We seek to generalize…