Zobrazeno 1 - 10
of 90
pro vyhledávání: '"Vrana, Peter"'
Asymptotic tensor rank is notoriously difficult to determine. Indeed, determining its value for the $2\times 2$ matrix multiplication tensor would determine the matrix multiplication exponent, a long-standing open problem. On the other hand, Strassen
Externí odkaz:
http://arxiv.org/abs/2411.15789
Autor:
Bugár, Dávid, Vrana, Péter
This paper explores the trade-off relation between the rate and the strong converse exponent for asymptotic LOCC transformations between pure multipartite states. Any single-copy probabilistic transformation between a pair of states implies that an a
Externí odkaz:
http://arxiv.org/abs/2409.01130
Autor:
Vrana, Péter
In a paper published in 1981, Sch\"onhage showed that large total matrix multiplications can be reduced to powers of partial matrix multiplication tensors, which correspond to the bilinear computation task of multiplying matrices with some of the ent
Externí odkaz:
http://arxiv.org/abs/2408.15728
Autor:
Bugár, Dávid, Vrana, Péter
The trade-off relation between the rate and the strong converse exponent for probabilistic asymptotic entanglement transformations between pure multipartite states can in principle be characterised in terms of a class of entanglement measures determi
Externí odkaz:
http://arxiv.org/abs/2309.11429
Autor:
Bugár, Dávid, Vrana, Péter
The asymptotic restriction problem for tensors can be reduced to finding all parameters that are normalized, monotone under restrictions, additive under direct sums and multiplicative under tensor products, the simplest of which are the flattening ra
Externí odkaz:
http://arxiv.org/abs/2208.14438
We give systematic ways of defining monotone quantum relative entropies and (multi-variate) quantum R\'enyi divergences starting from a set of monotone quantum relative entropies. Despite its central importance in information theory, only two additiv
Externí odkaz:
http://arxiv.org/abs/2207.14282
Autor:
Tasnádi, Tamás, Vrana, Péter
We propose a generalization of the asymptotic equipartition property to discrete sources with an ambiguous alphabet, and prove that it holds for irreducible stationary Markov sources with an arbitrary distinguishability relation. Our definition is ba
Externí odkaz:
http://arxiv.org/abs/2207.13789
Autor:
Vrana, Péter
The zero-error capacity of a classical channel is a parameter of its confusability graph, and is equal to the minimum of the values of graph parameters that are additive under the disjoint union, multiplicative under the strong product, monotone unde
Externí odkaz:
http://arxiv.org/abs/2207.10483
Publikováno v:
In Linear Algebra and Its Applications 15 October 2024 699:159-276
Autor:
Bunth, Gergely, Vrana, Péter
We study a generalization of relative submajorization that compares pairs of positive operators on representation spaces of some fixed group. A pair equivariantly relatively submajorizes another if there is an equivariant subnormalized channel that t
Externí odkaz:
http://arxiv.org/abs/2108.13217