Related papers: Quantum Optimal Transport
The accurate simulation of real--time quantum transport is notoriously difficult, requiring a consistent scheme to treat incoming and outgoing fluxes at the boundary of an open system. We demonstrate a method to converge non--equilibrium…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
This text is a set of lecture notes for a 4.5-hour course given at the Erd\"os Center (R\'enyi Institute, Budapest) during the Summer School "Optimal Transport on Quantum Structures" (September 19th-23rd, 2023). Lecture I introduces the…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
Using the dual formulation only, we show that the regularity of unbalanced optimal transport also called entropy-transport inherits from the regularity of standard optimal transport. We provide detailed examples of Riemannian manifolds and…
We study a nonlinear multimarginal optimal transport problem arising in risk management, where the objective is to maximize a spectral risk measure of the pushforward of a coupling by a cost function. Although this problem is inherently…
We demonstrate that among all quantum teleportation protocols giving rise to the same average fidelity, those with aligned Bloch vectors between input and output states exhibit the minimum average trace distance. This defines optimal…
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane $\R^2$. The key question is the optimality of the so-called Seidl map, first disproved by Colombo and Stra. We generalize the…
For quantum transport through mesoscopic system, a quantum master equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of…
We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system with bounded input. We completely solve the…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
In this paper, we analyze in a mathematically rigorous fashion the validity of the Boltzmann transport equation within quantum field theory. We work within the specific model of a hermitian, scalar field with polynomial self-interaction in…
Optimal Transport (OT) has fueled machine learning (ML) across many domains. When paired data measurements $(\boldsymbol{\mu}, \boldsymbol{\nu})$ are coupled to covariates, a challenging conditional distribution learning setting arises.…
Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…
In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov-Poisson equation, in the regime where the solutions have bounded…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
We study dynamical optimal transport metrics between density matrices associated to symmetric Dirichlet forms on finite-dimensional $C^*$-algebras. Our setting covers arbitrary skew-derivations and it provides a unified framework that…
We study a quantum analogue of the 2-Wasserstein distance as a measure of proximity on the set $\Omega_N$ of density matrices of dimension $N$. We show that such (semi-)distances do not induce Riemannian metrics on the tangent bundle of…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…