Leírás
Abstract:
Although the theory of classical optimal transport has been playing an important role in mathematical physics (especially in fluid dynamics) and probability since the late 80s, concepts of optimal transportation in quantum mechanics have emerged only very recently.
First, we briefly review two such concepts: one relying on quantum channels (pioneered by De Palma and Trevisan) and one relying on quantum couplings (pioneered by Caglioti, Golse, Mouhot, and Paul).
Then, we describe our progress in proving a conjecture of De Palma and Trevisan, saying that a smart modification of channel-based quantum Wasserstein distances gives rise to genuine metrics on quantum state spaces.
Finally, we describe the isometries of the qubit state space endowed with distinguished quantum Wasserstein distances.
The zoom link to the talk is:
https://us06web.zoom.us/j/83312342576?pwd=muM3vzOQ4nIezupfbcmNRI28855u9x.1