arXiv subjects

Sk Asfaq Hossain

Publications and source records attributed to Sk Asfaq Hossain.

4 recordsLinked to original sources

arXiv2026

A multigraph approach to confusability in quantum channels

We introduce a new approach to confusability in a quantum channel, namely quantum confusability multigraph, which incorporates the output information into the graphical structure. By``counting" the edges between two vertices of this confusability multigraph, one recovers the traditional confusability ``single-edged" graph of the channel. With this physical motivation, we therefore develop a theory of quantum multigraphs from Weaver's quantum relations point of view and explore its quantum graph theoretic properties. Finally, we provide a necessary and sufficient condition characterizing those quantum multigraphs that arise as quantum confusability multigraphs.

math.QA↗

arXiv2024

Quantum symmetry in multigraphs (part II)

This article is a continuation of "Quantum symmetry in multigraphs (part I)". In this article, we give an explicit construction of a non-Bichon type co-action on a multigraph that is, it preserves quantum symmetry of (V,E) in our sense but not always in Bichon's sense. This construction itself is motivated from automorphisms of quantum graphs.

math.QA↗

arXiv2024

Quantum symmetry in multigraphs (part I)

We introduce various notions of quantum symmetry in a directed or undirected multigraph with no isolated vertex and explore relations among them. If the multigraph is single edged (that is, a simple graph where loops are allowed), all our notions of quantum symmetry reduce to already existing notions of quantum symmetry provided by Bichon and Banica. Our constructions also show that any multigraph with at least two pairs of vertices with multiple edges among them possesses genuine quantum symmetry.

math.QA↗

arXiv2023

Quantum Symmetry on Potts Model

We formulate the notion of quantum group symmetry of the Hamiltonian corresponding to Potts model and compute it for few simple models. Our examples illustrate how a slight change of the model parameter may result in a drastic change of the quantum symmetry group, (in some cases, the classical symmetry group remains unaffected) signifying a case of phase transition.

math.QA↗