Optimal Transport on Quantum Structures
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Beschreibung
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.
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.
Contains lecture notes by leading experts in the field Gives an overview of the state of the art in non-commutative optimal transport Accessible to beginning researchers in the field
Autor*in
Jan Maas
Themen in »Optimal Transport on Quantum Structures«
Optimal transport Quantum states Gradient flows Quantum entropy Connes distance in non-commutative geometry Quantum structures Non-commutative mass transportation Quantum channels Quantum Wasserstein pseudo metric Quantum Kantorovich duality Quantum Gaussian channels Quantum optimal transport Many-body problems Wasserstein space Quantum Markov Semigroups