Related papers: Information-Theoretic Lower Bounds for Approximati…
We demonstrate that Shannon's information entropy and the thermodynamic entropy of Boltzmann and Gibbs are quantitatively equivalent for real condensed-matter systems. By interpreting atomic configurations as information sources, we compute…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
Information inequalities govern the ultimate limitations in information theory and as such play an pivotal role in characterizing what values the entropy of multipartite states can take. Proving an information inequality, however, quickly…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
$\mathtt{d}$-dimensional hyperspherical quantum dot with either Dirichlet or Neumann boundary conditions (BCs) allows analytic solution of the Schr\"{o}dinger equation in position space and the Fourier transform of the corresponding wave…
In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…
We derive an algorithm that achieves the optimal (within constants) pseudo-regret in both adversarial and stochastic multi-armed bandits without prior knowledge of the regime and time horizon. The algorithm is based on online mirror descent…
Although some information-theoretic measures of uncertainty or granularity have been proposed in rough set theory, these measures are only dependent on the underlying partition and the cardinality of the universe, independent of the lower…
In the approximate quantiles problem, the goal is to output $m$ quantile estimates, the ranks of which are as close as possible to $m$ given quantiles $0 \leq q_1 \leq\dots \leq q_m \leq 1$. We present a mechanism for approximate quantiles…
Analytic continuation of numerical data obtained in imaginary time or frequency has become an essential part of many branches of quantum computational physics. It is, however, an ill-conditioned procedure and thus a hard numerical problem.…
In this thesis, we present optimization tools for different problems in quantum information theory. First, we introduce an algorithm for quantum estate estimation. The algorithm consists of orthogonal projections on intersecting…
We introduce a new information-theoretic formulation of quantum measurement uncertainty relations, based on the notion of relative entropy between measurement probabilities. In the case of a finite-dimensional system and for any approximate…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
Subentropy is an entropy-like quantity that arises in quantum information theory; for example, it provides a tight lower bound on the accessible information for pure state ensembles, dual to the von Neumann entropy upper bound in Holevo's…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
We investigate localization transitions and mobility edge phenomena in one-dimensional quasiperiodic lattice models using an information theoretic framework based on the Tsallis entropy of single particle eigenstates.We employ the Tsallis…
Quantum information scrambling (QIS) is a characteristic feature of several quantum systems, ranging from black holes to quantum communication networks. While accurately quantifying QIS is crucial to understanding many such phenomena,…