9 papers
Strong Kantorovich duality for quantum optimal transport with generic cost and optimal couplings on quantum bits
Gergely Bunth, József Pitrik, Tamás Titkos +1
We prove Kantorovich duality for a linearized version of a recently proposed non-quadratic quantum optimal transport problem, where quantum channels realize the transport. As an ap…
Wasserstein distances and divergences of order by quantum channels
Gergely Bunth, József Pitrik, Tamás Titkos +1
We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincaré, {\bf 22} (2021), 3199-32…
The swap transpose on couplings translates to Petz' recovery map on quantum channels
Gergely Bunth, József Pitrik, Tamás Titkos +1
In [Ann. Henri Poincaré, {\bf 22} (2021), 3199-3234], De Palma and Trevisan described a one-to-one correspondence between quantum couplings and quantum channels realizing transpor…
Wasserstein Rigidity over with smooth norms
Zoltán M. Balogh, Eric Ströher, Tamás Titkos +1
We study Wasserstein spaces over equipped with a norm metric . We show that, if the norm is smooth enough, then the Wass…
Rigid and flexible Wasserstein spaces
Zoltán M. Balogh, Eric Ströher, Tamás Titkos +1
In this paper, we study isometries of -Wasserstein spaces. In our first result, for every complete and separable metric space and for every , we construct a metric s…
Isometric rigidity of the Wasserstein space over Carnot groups
Zoltán M. Balogh, Tamás Titkos, Dániel Virosztek
This paper aims to study isometries of the -Wasserstein space over Carnot groups endowed with horizontally strictly convex norms. Well-known examples…