We present a strong connection between quantum information and the theory of quantum
permutation groups. Specifically, we define a notion of quantum isomorphisms of graphs …

We introduce a notion of quantum function and develop a compositional framework for finite
quantum set theory based on a 2-category of quantum sets and quantum functions. We use …

We consider the hypercube in $\mathbb R^ n $, and show that its quantum symmetry group
is a $ q $-deformation of $ O_n $ at $ q=-1$. Then we consider the graph formed by $ n …

We classify the compact quantum groups acting on 4 points. These are the quantum
subgroups of the quantum permutation group 𝓠4. Our main tool is a new presentation for the …

This is a presentation of recent work on quantum permutation groups. Contains: a short
introduction to operator algebras and Hopf algebras; quantum permutation groups, and their …

We classify instances of quantum pseudo-telepathy in the graph isomorphism game,
exploiting the recently discovered connection between quantum information and the theory …

This is a transcript of a series of eight lectures, 90 min each, held at IMSc Chennai, India
from 5–24 January 2015. We give basic definitions, properties and examples of compact …

In this article, we study quantum automorphism groups of distance-transitive graphs. We
show that the odd graphs, the Hamming graphs H (n, 3), the Johnson graphs J (n, 2) and the …

The study of graph-algebra. In our result, we use the definition of quantum automorphism
groups of graphs as given by Banica in 2005. Note that Bichon gave a different definition in …

The concept of quantum automorphism groups of finite graphs was introduced by Banica
and Bichon in [1, 9]. It generalizes the classical automorphism groups of graphs within the …