9 citations · 17 across the 11 of their papers we have counts for
12 papers
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 transport…
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…
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…
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…
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), 3199-323…
Isometries of the qubit state space with respect to quantum Wasserstein distances
Richárd Simon, Dániel Virosztek
In this paper we study isometries of quantum Wasserstein distances and divergences on the quantum bit state space. We describe isometries with respect to the symmetric quantum Wass…
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…
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…
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…
On algebraic endomorphisms of the Einstein gyrogroup
Lajos Molnár, Dániel Virosztek
We describe the structure of all continuous algebraic endomorphisms of the open unit ball of equipped with the Einstein velocity addition. We show that…