Quantum Optimal Transport: Quantum Channels and Qubits - Part 1 of 3

In this lecture, Dario Trevisan from the Università di Pisa presents the first part of a three-part tutorial on "Quantum Optimal Transport: Quantum Channels and Qubits" at IPAM's Non-commutative Optimal Transport Tutorials at UCLA. Explore two key approaches to quantum optimal transport: one using quantum channels as generalized transport plans and another based on the Hamming-Wasserstein distance of order 1 on multiple-qubit systems. The material is presented in an accessible manner, focusing on finite-dimensional settings with illustrative examples. Recorded on March 11, 2025, this 1-hour and 17-minute presentation serves as an introduction to the topic, making complex quantum transport concepts approachable for viewers with relevant background knowledge.