@misc{MTMT:34131047, title = {Isometric rigidity of Wasserstein spaces over Euclidean spheres}, url = {https://m2.mtmt.hu/api/publication/34131047}, author = {Gehér, György and Hruskova, Aranka and Titkos, Tamás and Virosztek, Dániel}, unique-id = {34131047}, year = {2023}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:33678624, title = {On isometries of Wasserstein spaces}, url = {https://m2.mtmt.hu/api/publication/33678624}, author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel}, journal-iso = {RIMS KOKYUROKU BESSATSU}, journal = {RIMS KOKYUROKU BESSATSU}, volume = {B93}, unique-id = {33678624}, issn = {1881-6193}, year = {2023}, pages = {239-250}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:33578758, title = {Isometric rigidity of Wasserstein tori and spheres}, url = {https://m2.mtmt.hu/api/publication/33578758}, author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel}, doi = {10.1112/mtk.12174}, journal-iso = {MATHEMATIKA}, journal = {MATHEMATIKA}, volume = {69}, unique-id = {33578758}, issn = {0025-5793}, abstract = {We prove isometric rigidity for p-Wasserstein spaces over finite-dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials. © 2022 The Authors. The publishing rights in this article are licensed to University College London under an exclusive licence. Mathematika is published by the London Mathematical Society on behalf of University College London.}, year = {2023}, eissn = {2041-7942}, pages = {20-32}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:33578756, title = {Quantum Wasserstein isometries on the qubit state space}, url = {https://m2.mtmt.hu/api/publication/33578756}, author = {Gehér, György and Pitrik, József and Titkos, Tamás and Virosztek, Dániel}, doi = {10.1016/j.jmaa.2022.126955}, journal-iso = {J MATH ANAL APPL}, journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS}, volume = {522}, unique-id = {33578756}, issn = {0022-247X}, abstract = {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 the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model this means that the isometry group coincides with the classical symmetry group O(3). On the other hand, for the cost generated by the qubit ‘‘clock” and ‘‘shift” operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. © 2022 Elsevier Inc.}, keywords = {isometries; Quantum bits; Quantum optimal transport}, year = {2023}, eissn = {1096-0813}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:31855431, title = {The isometry group of Wasserstein spaces: the Hilbertian case}, url = {https://m2.mtmt.hu/api/publication/31855431}, author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel}, doi = {10.1112/jlms.12676}, journal-iso = {J LOND MATH SOC}, journal = {JOURNAL OF THE LONDON MATHEMATICAL SOCIETY}, volume = {106}, unique-id = {31855431}, issn = {0024-6107}, abstract = {Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space (Formula presented.), we describe the isometry group (Formula presented.) for all parameters (Formula presented.) and for all separable real Hilbert spaces (Formula presented.). In particular, we show that (Formula presented.) is isometrically rigid for all Polish space (Formula presented.) whenever (Formula presented.). This is a consequence of our more general result: we prove that (Formula presented.) is isometrically rigid if (Formula presented.) is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters (Formula presented.), by solving Kloeckner's problem affirmatively on the existence of mass-splitting isometries. As a byproduct of our methods, we also obtain the isometric rigidity of (Formula presented.) for all complete and separable ultrametric spaces (Formula presented.) and parameters (Formula presented.). © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.}, year = {2022}, eissn = {1469-7750}, pages = {3836-3894}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:31846405, title = {Entanglement entropy of two disjoint intervals separated by one spin in a chain of free fermion}, url = {https://m2.mtmt.hu/api/publication/31846405}, author = {Brightmore, L and Gehér, György and Its, A R and Korepin, V E and Mezzadri, F and Mo, M Y and Virtanen, J A}, doi = {10.1088/1751-8121/ab9cf2}, journal-iso = {J PHYS A-MATH THEOR}, journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}, volume = {53}, unique-id = {31846405}, issn = {1751-8113}, year = {2020}, eissn = {1751-8121}, pages = {345303}, orcid-numbers = {Gehér, György/0000-0003-1499-3229; Mezzadri, F/0000-0002-4572-5617} } @article{MTMT:31690523, title = {Coexistency on Hilbert Space Effect Algebras and a Characterisation of Its Symmetry Transformations}, url = {https://m2.mtmt.hu/api/publication/31690523}, author = {Gehér, György and Semrl, Peter}, doi = {10.1007/s00220-020-03873-3}, journal-iso = {COMMUN MATH PHYS}, journal = {COMMUNICATIONS IN MATHEMATICAL PHYSICS}, volume = {379}, unique-id = {31690523}, issn = {0010-3616}, abstract = {The Hilbert space effect algebra is a fundamental mathematical structure which is used to describe unsharp quantum measurements in Ludwig's formulation of quantum mechanics. Each effect represents a quantum (fuzzy) event. The relation of coexistence plays an important role in this theory, as it expresses when two quantum events can be measured together by applying a suitable apparatus. This paper's first goal is to answer a very natural question about this relation, namely, when two effects are coexistent with exactly the same effects? The other main aim is to describe all automorphisms of the effect algebra with respect to the relation of coexistence. In particular, we will see that they can differ quite a lot from usual standard automorphisms, which appear for instance in Ludwig's theorem. As a byproduct of our methods we also strengthen a theorem of Molnar.}, year = {2020}, eissn = {1432-0916}, pages = {1077-1112}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:31161216, title = {Isometric study of Wasserstein spaces - the real line,}, url = {https://m2.mtmt.hu/api/publication/31161216}, author = {Gehér, György and Virosztek, Dániel and Titkos, Tamás}, doi = {10.1090/tran/8113}, journal-iso = {T AM MATH SOC}, journal = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, volume = {373}, unique-id = {31161216}, issn = {0002-9947}, abstract = {The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where X is a countable discrete metric space and 0}, year = {2020}, eissn = {1088-6850}, pages = {5855-5883}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:31146441, title = {Symmetries of Projective Spaces and Spheres}, url = {https://m2.mtmt.hu/api/publication/31146441}, author = {Gehér, György}, doi = {10.1093/imrn/rny100}, journal-iso = {INT MATH RES NOTICES}, journal = {INTERNATIONAL MATHEMATICS RESEARCH NOTICES}, volume = {2020}, unique-id = {31146441}, issn = {1073-7928}, abstract = {Let H be either a complex inner product space of dimension at least two or a real inner product space of dimension at least three, and let us fix an alpha is an element of(0, pi/2). The purpose of this paper is to characterise all bijective transformations on the projective space P(H) which preserve the quantum angle alpha (or Fubini-Study distance alpha) between lines in both directions. (Let us emphasise that we do not assume anything about the preservation of other quantum angles). For real inner product spaces and when H = C-2 we do this for every alpha, and when H is a complex inner product space of dimension at least three we describe the structure of such transformations for alpha <= pi/4. Our result immediately gives an Uhlhorn-type generalisation of Wigner's theorem on quantum mechanical symmetry transformations, that is considered to be a cornerstone of the mathematical foundations of quantum mechanics. Namely, under the above assumptions, every bijective map on the set of pure states of a quantum mechanical system that preserves the transition probability cos(2) alpha in both directions is a Wigner symmetry (thus automatically preserves all transition probabilities), except for the case when H = C-2 and alpha = pi/4 where an additional possibility occurs. (Note that the classical theorem of Uhlhorn is the solution for the alpha = pi/2 case). Usually in the literature, results which are connected to Wigner's theorem are discussed under the assumption of completeness of H; however, here we shall remove this unnecessary hypothesis in our investigation. Our main tool is a characterisation of bijective maps on unit spheres of real inner product spaces which preserve one spherical angle in both directions.}, year = {2020}, eissn = {1687-0247}, pages = {2205-2240}, orcid-numbers = {Gehér, György/0000-0003-1499-3229} } @article{MTMT:31033608, title = {Maps preserving absolute continuity and singularity of positive operators}, url = {https://m2.mtmt.hu/api/publication/31033608}, author = {Gehér, György and Tarcsay, Zsigmond and Titkos, Tamás}, journal-iso = {NEW YORK J MATH}, journal = {NEW YORK JOURNAL OF MATHEMATICS}, volume = {26}, unique-id = {31033608}, issn = {1076-9803}, year = {2020}, pages = {129-137}, orcid-numbers = {Gehér, György/0000-0003-1499-3229; Tarcsay, Zsigmond/0000-0001-8102-5055} }