Perfect state transfer over interacting boson networks associated with group schemes

It is shown how to perfectly transfer an arbitrary qudit state in interacting boson networks. By defining a family of Hamiltonians related to Bose-Hubbard model, we describe a possible method for state transfer through bosonic atoms trapped in these networks with different kinds of coupling strengths between them. Particularly, by taking the underlying networks of so called group schemes as interacting boson networks, we show how choose suitable coupling strengths between the nodes, in order that an arbitrary qudit state be transferred from one node to its antipode, perfectly. In fact, by employing the group theory properties of these networks, an explicit formula for suitable coupling strengths has been given in order that perfect state transfer (PST) be achieved. Finally, as examples, PST on the underlying networks associated with cyclic group C2m, dihedral group D2n, Clifford group CL(n), and the groups U6n and V8n has been considered in details. Keywords: Bose-Hubbard Hamiltonian, Interacting boson networks, Perfect state transfer (PST), Qudit state, Underlying networks, Group schemes PACs Index: 01.55.+b, 02.10.Yn