8 papers
Topological and Geometric Perspectives on Homomorphism Indistinguishability
Josse van Dobben de Bruyn, Jérémie Marquès, David E. Roberson +3
Two graphs and are homomorphism indistinguishable over a graph class if, for every graph , the number of homomorphisms from to is e…
Mermin-Peres magic rectangles modulo odd primes
Josse van Dobben de Bruyn, Remy van Dobben de Bruyn, Peter Zeman
The Mermin-Peres magic square provides a simple example of a system of linear equations over which has no classical solutions but does have a finite-dimens…
Quantum polymorphism characterisation of commutativity gadgets in all quantum models
Eric Culf, Josse van Dobben de Bruyn, Peter Zeman
Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal g…
Existence and nonexistence of commutativity gadgets for entangled CSPs
Eric Culf, Josse van Dobben de Bruyn, Matthijs Vernooij +1
Commutativity gadgets allow NP-hardness proofs for classical constraint satisfaction problems (CSPs) to be carried over to undecidability proofs for the corresponding entangled CSP…
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…
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…
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…