TY  - BOOK
AU  - Maas,Jan
AU  - Rademacher,Simone
AU  - Titkos,Tamás
AU  - Virosztek,Dániel
ED  - SpringerLink (Online service)
TI  - Optimal Transport on Quantum Structures
T2  - Bolyai Society Mathematical Studies,
SN  - 9783031504662
AV  - QA1-939 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Mathematics
KW  - Mathematical analysis
KW  - Global analysis (Mathematics)
KW  - Manifolds (Mathematics)
KW  - Measure theory
KW  - Analysis
KW  - Global Analysis and Analysis on Manifolds
KW  - Measure and Integration
N1  - Preface -- Chapter 1. An Introduction to Optimal Transport and Wasserstein Gradient Flows by Alessio Figalli -- Chapter 2. Dynamics and Quantum Optimal Transport:Three Lectures on Quantum Entropy and Quantum Markov Semigroups by Eric A. Carlen -- Chapter 3. Quantum Couplings and Many-body Problems by Francois Golse -- Chapter 4. Quantum Channels and Qubits by Giacomo De Palma and Dario Trevisan -- Chapter 5. Entropic Regularised Optimal Transport in a Noncommutative Setting by Lorenzo Portinale -- Chapter 6. Logarithmic Sobolev Inequalities for Finite Dimensional Quantum Markov Chains by Cambyse Rouzé
N2  - The flourishing theory of classical optimal transport concerns mass transportation at minimal cost. This book introduces the reader to optimal transport on quantum structures, i.e., optimal transportation between quantum states and related non-commutative concepts of mass transportation. It contains lecture notes on classical optimal transport and Wasserstein gradient flows dynamics and quantum optimal transport quantum couplings and many-body problems quantum channels and qubits These notes are based on lectures given by the authors at the "Optimal Transport on Quantum Structures" School held at the Erdös Center in Budapest in the fall of 2022. The lecture notes are complemented by two survey chapters presenting the state of the art in different research areas of non-commutative optimal transport
UR  - https://doi.org/10.1007/978-3-031-50466-2
ER  -