14 citations · 76 across the 23 of their papers we have counts for
29 papers
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…
Isometric rigidity of the Wasserstein space over the plane with the maximum metric
Zoltán M. Balogh, Gergely Kiss, Tamás Titkos +1
We study -Wasserstein spaces over the branching spaces and equipped with the maximum norm metric. We show that these spaces are isometrically rigid for…
Isometries of Lipschitz-free Banach spaces
Marek Cúth, Michal Doucha, Tamás Titkos
We describe surjective linear isometries and linear isometry groups of a large class of Lipschitz-free spaces that includes e.g. Lipschitz-free spaces over any graph. We define the…
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…
Isometric rigidity of Wasserstein spaces over Euclidean spheres
György Pál Gehér, Aranka Hrušková, Tamás Titkos +1
We study the structure of isometries of the quadratic Wasserstein space over the sphere endowed with the distance inherited from…
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…
Isometries and isometric embeddings of Wasserstein spaces over the Heisenberg group
Zoltán M. Balogh, Tamás Titkos, Dániel Virosztek
Our purpose in this paper is to study isometries and isometric embeddings of the -Wasserstein space over the Heisenberg group for al…
Quantum Wasserstein isometries on the qubit state space
György Pál Gehér, József Pitrik, Tamás Titkos +1
We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all t…
Isometric rigidity of Wasserstein tori and spheres
György Pál Gehér, Tamás Titkos, Dániel Virosztek
We prove isometric rigidity for -Wasserstein spaces over finite-dimensional tori and spheres for all . We present a unified approach to proving rigidity that relies on the ro…
Isometric rigidity of Wasserstein spaces: the graph metric case
Gergely Kiss, Tamás Titkos
The aim of this paper is to prove that the -Wasserstein space is isometrically rigid for all whenever is a countable graph metric space. As a co…
The isometry group of Wasserstein spaces: the Hilbertian case
György Pál Gehér, Tamás Titkos, Dániel Virosztek
Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space , we describe the isometry group $\mathrm{Isom}\lef…
Operators on anti-dual pairs: self-adjoint extensions and the Strong Parrott Theorem
Zsigmond Tarcsay, Tamás Titkos
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it c…
Operators on anti-dual pairs: Generalized Schur complement
Zsigmond Tarcsay, Tamás Titkos
The goal of this paper is to develop the theory of Schur complementation in the context of operators acting on anti-dual pairs. As a byproduct, we obtain a natural generalization o…
Isometric study of Wasserstein spaces --- the real line
György Pál Gehér, Tamás Titkos, Dániel Virosztek
Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space . It turned out that the case of the rea…
Operators on anti-dual pairs: Generalized Krein--von Neumann extension
Zsigmond Tarcsay, Tamás Titkos
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert sp…
On isometric embeddings of Wasserstein spaces -- the discrete case
György Pál Gehér, Tamás Titkos, Dániel Virosztek
The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space ,…
Quasi-units as orthogonal projections
Zsigmond Tarcsay, Tamás Titkos
The notion of quasi-unit has been introduced by Yosida in unital Riesz spaces. Later on, a fruitful potential theoretic generalization was obtained by Arsove and Leutwiler. Due to…
A characterization of positive normal functionals on the full operator algebra
Zoltán Sebestyén, Zsigmond Tarcsay, Tamás Titkos
Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full opera…
A characterisation of isometries with respect to the Lévy-Prokhorov metric
György Pál Gehér, Tamás Titkos
According to the fundamental work of Yu.V. Prokhorov, the general theory of stochastic processes can be regarded as the theory of probability measures in complete separable metric…
Arlinskii's iteration and its applications
Tamás Titkos
Several Lebesgue-type decomposition theorems in analysis have a strong relation to the operation called: parallel sum. The aim of this paper is to investigate this relation from a…