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Optimal Transport on Quantum Structures
Paperback
Series: Bolyai Society Mathematical Studies, Book 29
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ISBN13: 9783031504686
Publisher: Springer
Published: Sep 20 2025
Pages: 321
Language: English
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.
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