Related papers: A Mirror-Descent Algorithm for Computing the Petz-…
We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical…
We study commitment scheme for classical-quantum channels. To accomplish this we define various notions of commitment capacity for these channels and prove matching upper and lower bound on it in terms of the conditional entropy. Our…
Quantum computing has the potential to outperform classical computers and is expected to play an active role in various fields. In quantum machine learning, a quantum computer has been found useful for enhanced feature representation and…
We show that the quantum $\alpha$-relative entropies with parameter $\alpha\in (0,1)$ can be represented as generalized cutoff rates in the sense of [I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, (1995)], which provides a direct…
Given two density matrices $\rho$ and $\sigma$, there are a number of different expressions that reduce to the $\alpha$-R\'enyi relative entropy of $\rho$ with respect to $\sigma$ in the classical case; i.e., when $\rho$ and $\sigma$…
In this article we introduce an algorithm for mitigating the adverse effects of noise on gradient descent in variational quantum algorithms. This is accomplished by computing a {\emph{regularized}} local classical approximation to the…
In this paper, we propose a Bregman frame for several classical alternating minimization algorithms. In the frame, these algorithms have uniform mathematical formulation. We also present convergence analysis for the frame algorithm. Under…
We propose an iterative method for approximating the capacity of classical-quantum channels with a discrete input alphabet and a finite dimensional output, possibly under additional constraints on the input distribution. Based on duality of…
Explicit classical states achieving maximal $f$-divergence are given, allowing for a simple proof of Matsumoto's Theorem, and the systematic extension of any inequality between classical $f$-divergences to quantum $f$-divergences. Our…
We consider Calabi-Yau compactifications with one K\"ahler modulus. Following the method of Candelas et al. we use the mirror hypothesis to solve the quantum theory exactly in dependence of this modulus by performing the calculation for the…
We present a new perspective on the celebrated Sinkhorn algorithm by showing that is a special case of incremental/stochastic mirror descent. In order to see this, one should simply plug Kullback-Leibler divergence in both mirror map and…
This paper focuses on $\alpha$-divergence minimisation methods for Variational Inference. More precisely, we are interested in algorithms optimising the mixture weights of any given mixture model, without any information on the underlying…
We present a method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements (i.e. without complete process tomography), reconstruction of sets of conditional probabilities, and…
The dual tasks of quantum Hamiltonian learning and quantum Gibbs sampling are relevant to many important problems in physics and chemistry. In the low temperature regime, algorithms for these tasks often suffer from intractabilities, for…
A recent method to certify the classical capacity of quantum communication channels is applied for general damping channels in finite dimension. The method compares the mutual information obtained by coding on the computational and a…
Computing the classical capacity of a noisy quantum channel is crucial for understanding the limits of communication over quantum channels. However, its evaluation remains challenging due to the difficulty of computing the Holevo capacity…
Estimation of Shannon and R\'enyi entropies of unknown discrete distributions is a fundamental problem in statistical property testing and an active research topic in both theoretical computer science and information theory. Tight bounds on…
We study the convergence issue for the gradient algorithm (employing general step sizes) for optimization problems on general Riemannian manifolds (without curvature constraints). Under the assumption of the local convexity/quasi-convexity…
The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function,…
We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…