Talk 1.   On distances in the space of quantum states

Various distances between two quantum states are discussed. Some properties and meaning of the trace, Hilbert-Schmidt and Bures distances and Bures angle related to fidelity will be reviewed, and some useful bounds will be given. More recent results on the transmission distance (square root of the Jensen-Shannon divergence) and the transport distance, related to the Earth-Mover distance of Monge-Kantorovich will also be presented [1]. It is fair to expect that these different distances will find their applications in quantum information and machine learning.

[1] S. Friedland, M. Eckstein, S. Cole and K. Życzkowski, Quantum Monge-Kantorovich problem and transport distance between density matrices, preprint arXiv:2102.07787