11 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…
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…
Restoring Wasserstein Rigidity with a single point
Zoltán M. Balogh, Eric Ströher, Dániel Virosztek
We consider isometrically flexible Wasserstein spaces and demonstrate that adding a single point to the underlying metric space makes these Wasserstein spaces rigid.
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…