7 papers · 1 filter
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…
Quantum Wasserstein isometries of the -qubit state space: a Wigner-type result
Gergely Bunth, Eszter Szabó, Dániel Virosztek
We determine the isometry group of the -qubit state space with respect to the quantum Wasserstein distance induced by the so-called symmetric transport cost for all $n \in \math…
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…
Limit theorems for empirical measures of interacting quantum systems in Wasserstein space
Lorenzo Portinale, Simone Rademacher, Dániel Virosztek
We prove fundamental properties of empirical measures induced by measurements performed on quantum -body systems. More precisely, we consider measurements performed on the groun…
On the metric property of quantum Wasserstein divergences
Gergely Bunth, József Pitrik, Tamás Titkos +1
Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces b…