6 papers
Quantum Optimal Transport Barycenters: Existence, Duality, and Gaussian Rigidity
Augusto Gerolin, Zhiyi Lin
We develop a Quantum Optimal Transport (QOT) barycenter framework for quantum states, as an analog of Wasserstein barycenters~\cite{AguCar}, and establish existence and duality res…
Quantum thermodynamics and semidefinite programming: regularization and algorithms
Emanuele Caputo, Augusto Gerolin, Nataliia Monina +2
We investigate variational problems in quantum thermodynamics at positive temperature, in which admissible states are constrained by prescribed outcomes of a finite set of measurem…
Quantum Wasserstein distance for Gaussian states
Anaelle Hertz, Mohammad Ahmadpoor, Oleksandr Dzhenzherov +2
Optimal transport between classical probability distributions has been proven useful in areas such as machine learning and random combinatorial optimization. Quantum optimal transp…
Quantum optimal transport with convex regularization
Emanuele Caputo, Augusto Gerolin, Nataliia Monina +1
The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We cons…
Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost
Augusto Gerolin, Mircea Petrache, Adolfo Vargas-Jimenez
We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we…
Non-commutative Optimal Transport for semi-definite positive matrices
Augusto Gerolin, Nataliia Monina
We introduce the von Neumann entropy regularization of Unbalanced Non-commutative Optimal Transport, specifically Non-commutative Optimal Transport between semi-definite positive m…