Related papers: An optimal problem for relative entropy
We define a one-parameter family of entropies, each assigning a real number to any probability measure on a compact metric space (or, more generally, a compact Hausdorff space with a notion of similarity between points). These entropies…
We study optimal perfect distinguishability between a unitary and a general quantum operation. In 2-dimensional case we provide a simple sufficient and necessary condition for sequential perfect distinguishability and an analytical formula…
Uhlmann's theorem states that, for any two quantum states $\rho_{AB}$ and $\sigma_A$, there exists an extension $\sigma_{AB}$ of $\sigma_A$ such that the fidelity between $\rho_{AB}$ and $\sigma_{AB}$ equals the fidelity between their…
We revisit the following problem (along with its higher dimensional variant): Given a set $S$ of $n$ points inside an axis-parallel rectangle $U$ in the plane, find a maximum-area axis-parallel sub-rectangle that is contained in $U$ but…
Optimal control theory is a powerful tool for improving figures of merit in quantum information tasks. Finding the solution to any optimal control problem via numerical optimization depends crucially on the choice of the optimization…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that maximum entropy is a universally Bayes optimal decision rule…
We present a formula for the relative entropy S(rho||sigma) of two n mode gaussian states rho, sigma in the boson Fock space. It is shown that the relative entropy has a classical and a quantum part: The classical part consists of a…
The relative entropy of entanglement is defined in terms of the relative entropy between an entangled state and its closest separable state (CSS). Given a multipartite-state on the boundary of the set of separable states, we find a closed…
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.…
We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
The problem of order execution is cast as a relative entropy-regularized robust optimal control problem in this article. The order execution agent's goal is to maximize an objective functional associated with his profit-and-loss of trading…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
In this work, we use the theory of quantum states over time to define an entropy $S(\rho,\mathcal{E})$ associated with quantum processes $(\rho,\mathcal{E})$, where $\rho$ is a state and $\mathcal{E}$ is a quantum channel responsible for…
Our capacity to process information depends on the computational power at our disposal. Information theory captures our ability to distinguish states or communicate messages when it is unconstrained with unrivaled beauty and elegance. For…
We shall consider a stochastic maximum principle of optimal control for a control problem associated with a stochastic partial differential equations of the following type: d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt +…
This work explores connections between the quantum relative entropy of two faithful states $\rho,\sigma$ (i.e. full-rank density matrices) and the Kullback-Leibler divergences of classical measures $\mu,\nu$. Here, $\mu$ and $\nu$ are…
Quantum information theory, particularly its entropic formulations, has made remarkable strides in characterizing quantum systems and tasks. However, a critical dimension remains underexplored: computational efficiency. While classical…