Related papers: Fermionic optimal transport
A quadratic optimal transport metric on the set of probability measure over $\R^2$ is introduced. The quadratic cost is given by the euclidean norm on $\R^2$ associated to some well chosen symmetric positive matrix, which makes the metric…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
Given two rational univariate polynomials, the Wasserstein distance of their associated measures is an algebraic number. We determine the algebraic degree of the squared Wasserstein distance, serving as a measure of algebraic complexity of…
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. Our algorithm is built on multilevel primal-dual…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
Optimal transport is widely used in pure and applied mathematics to find probabilistic solutions to hard combinatorial matching problems. We extend the Wasserstein metric and other elements of optimal transport from the matching of sets to…
This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou-Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport.…
Transport equations for autonomous driven Fermionic quantum systems are derived with the help of statistical assumptions and of the Markov approximation. The statistical assumptions hold if the system consists of subsystems within which…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…
In this paper, we describe a possible generalization of the Wasserstein 2-metric, originally defined on the space of scalar probability densities, to the space of Hermitian matrices with trace one, and to the space of matrix-valued…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
We introduce a new class of distances between nonnegative Radon measures in Euclidean spaces. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou-Brenier and provide a…
Traditional theories of electron transport in crystals are based on the Boltzmann equation and do not capture physics arising from quantum coherence. We introduce a transport formalism based on ''orbital Wigner functions'', which accurately…
Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the…
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $\mathbb{Z}^d$, which we call specific quantum $W_1$ distance. The proposal is based on the $W_1$ distance for qudits of [De Palma et…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…