6 papers
Free Inhomogeneous Wreath Product of Quantum Groups
Josse van Dobben de Bruyn, Amaury Freslon, Prem Nigam Kar +2
We introduce the free inhomogeneous wreath product of compact matrix quantum groups, which generalizes the free wreath product (Bichon 2004). We use this to present a general techn…
Robust Self-testing for Synchronous Correlations and Games
Prem Nigam Kar
We develop an abstract operator-algebraic characterization of robust self-testing for synchronous correlations and games. Specifically, we show that a synchronous correlation is a…
NPA Hierarchy for Quantum Isomorphism and Homomorphism Indistinguishability
Prem Nigam Kar, David E. Roberson, Tim Seppelt +1
Mančinska and Roberson [FOCS'20] showed that two graphs are quantum isomorphic if and only if they admit the same number of homomorphisms from any planar graph. Atserias et al. [JC…
Quantum Sabidussi's Theorem
Arnbjörg Soffía Árnadóttir, Josse van Dobben de Bruyn, Prem Nigam Kar +2
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 produ…
Transitive Nonlocal Games
Prem Nigam Kar, Jitendra Prakash, David E Roberson
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 bisynchr…
Quantum automorphism groups of trees
Josse van Dobben de Bruyn, Prem Nigam Kar, David E. Roberson +2
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 pr…