I am an associate professor at the Department of Geometry within the Institute of Mathematics of the Budapest University of Technology and Economics. Previously, I was a postdoctoral researcher at ETH Zurich and at the Technical University of Munich. I recieved my PhD from the Doctoral School of Physics, Budapest University of Technology and Economics.

In 2019 I was awarded a János Bolyai Research Scholarship of the Hungarian Academy of Sciences.

My main research interest is in mathematical aspects of quantum information theory, especially asymptotic transformations in entanglement theory and other resource theories. In my work I use tools from various areas of mathematics, including representation theory, information theory, and matrix analysis.

## Most important publications

- Péter Vrana, A family of multipartite entanglement measures
*Communications in Mathematical Physics*, 402(1):637–664, 2023

arXiv, doi - Matthias Christandl, Péter Vrana, and Jeroen Zuiddam, Universal points in the asymptotic spectrum of tensors
*Journal of the American Mathematical Society*, 36:31–79, 2023

arXiv, doi - Péter Vrana, Asymptotic continuity of additive entanglement measures
*IEEE Transactions on Information Theory*, 68(5):3208–3217, 2022

arXiv, doi - Christopher Perry, Péter Vrana, and Albert H Werner, The semiring of dichotomies and asymptotic relative submajorization
*IEEE Transactions on Information Theory*, 68(1):311–321, 2022

arXiv, doi - Matthias Christandl, Péter Vrana, and Jeroen Zuiddam, Barriers for fast matrix multiplication from irreversibility
*Theory of Computing*, 17(2):1–32, 2021

arXiv, doi - Péter Vrana, Probabilistic refinement of the asymptotic spectrum of graphs
*Combinatorica*, 41:873–904, 2021

arXiv, doi - Alonso Botero, Matthias Christandl, and Péter Vrana, Large deviation principle for moment map estimation
*Electronic Journal of Probability*, 26:1–23, 2021

arXiv, doi - Péter Vrana and Matthias Christandl, Distillation of Greenberger–Horne–Zeilinger states by combinatorial methods
*IEEE Transactions on Information Theory*, 65(9):5945–5958, 2019

arXiv, doi - Asger Kjærulff Jensen and Péter Vrana, The asymptotic spectrum of LOCC transformations
*IEEE Transactions on Information Theory*, 66(1):155–166, 2019

arXiv, doi - Péter Vrana and Matthias Christandl, Entanglement distillation from Greenberger–Horne–Zeilinger shares
*Communications in Mathematical Physics*, 352(2):621–627, 2017

arXiv, doi