Aula Galilei (ex-131), Ground Floor, Building C, Polo Fibonacci (Pisa)
Speaker: Dario Trevisan (Dipartimento di Matematica – Universita` di Pisa)
Title: “The quantum Wasserstein distance of order 1 (earth mover’s distance) and applications”
Abstract:
In this talk I will describe a recently proposed a generalization of the Wasserstein distance of order 1 to the quantum states of n qubits, based on a joint work with G. De Palma, M. Marvian and S. Lloyd. Our proposal recovers the Hamming distance for the vectors of the canonical basis, and more generally the classical Wasserstein distance for quantum states diagonal in the canonical basis. Our main result is a continuity bound for the von Neumann entropy with respect to the proposed distance, which significantly strengthens the best continuity bound with respect to the trace distance. Moreover, we derive bounds on the contraction coefficients of shallow quantum circuits and of the tensor product of one-qubit quantum channels with respect to the proposed distance. We discuss possible applications in quantum machine learning, quantum Shannon theory, and quantum many-body systems, some of which have been considered in recent literature.