Zobrazeno 1 - 10
of 705
pro vyhledávání: '"Roberson, David A."'
Man\v{c}inska and Roberson~[FOCS'20] showed that two graphs are quantum isomorphic if and only if they are homomorphism indistinguishable over the class of planar graphs. Atserias et al.~[JCTB'19] proved that quantum isomorphism is undecidable in gen
Externí odkaz:
http://arxiv.org/abs/2407.10635
Autor:
Árnadóttir, Arnbjörg Soffía, de Bruyn, Josse van Dobben, Kar, Prem Nigam, Roberson, David E., Zeman, Peter
Sabidussi's theorem [Duke Math. J. 28, 1961] gives necessary and sufficient conditions under which the automorphism group of a lexicographic product of two graphs is a wreath product of the respective automorphism groups. We prove a quantum version o
Externí odkaz:
http://arxiv.org/abs/2402.12344
We study a class of nonlocal games, called transitive games, for which the set of perfect strategies forms a semigroup. We establish several interesting correspondences of bisynchronous transitive games with the theory of compact quantum groups. In p
Externí odkaz:
http://arxiv.org/abs/2312.12040
Autor:
de Bruyn, Josse van Dobben, Kar, Prem Nigam, Roberson, David E., Schmidt, Simon, Zeman, Peter
We give a characterisation of quantum automorphism groups of trees. In particular, for every tree, we show how to iteratively construct its quantum automorphism group using free products and free wreath products. This can be considered a quantum vers
Externí odkaz:
http://arxiv.org/abs/2311.04891
We present a sequence of finite graphs with trivial automorphism group and non-trivial quantum automorphism group, which are the first known examples of graphs with this property. The examples are based on solution groups to (binary) linear systems.
Externí odkaz:
http://arxiv.org/abs/2311.04889
Autor:
Roberson, David E., Seppelt, Tim
Publikováno v:
TheoretiCS, Volume 3 (September 2, 2024) theoretics:12321
We show that feasibility of the $t^\text{th}$ level of the Lasserre semidefinite programming hierarchy for graph isomorphism can be expressed as a homomorphism indistinguishability relation. In other words, we define a class $\mathcal{L}_t$ of graphs
Externí odkaz:
http://arxiv.org/abs/2302.10538
Autor:
Roberson, David E.
We introduce (weak) oddomorphisms of graphs which are homomorphisms with additional constraints based on parity. These maps turn out to have interesting properties (e.g., they preserve planarity), particularly in relation to homomorphism indistinguis
Externí odkaz:
http://arxiv.org/abs/2206.10321
Autor:
Roberson, David, Schmidt, Simon
Publikováno v:
Journal of the London Mathematical Society, 2022
In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that the quantu
Externí odkaz:
http://arxiv.org/abs/2111.12362
Autor:
Roberson, David E., Schmidt, Simon
We introduce the notion of nonlocal symmetry of a graph $G$, defined as a winning quantum correlation for the $G$-automorphism game that cannot be produced classically. Recent connections between quantum group theory and quantum information show that
Externí odkaz:
http://arxiv.org/abs/2012.13328
Autor:
Roberson, David E., Izumi, Shuro, Roga, Wojciech, Neergaard-Nielsen, Jonas S., Takeoka, Masahiro, Andersen, Ulrik L.
Publikováno v:
Phys. Rev. A 103, 022423 (2021)
We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider t
Externí odkaz:
http://arxiv.org/abs/2009.00108