Abstract
In this paper, we study the generation of Bell states between distant vertices in apermanently coupled quantum spin network, interacting via invariant stratification graphs.To begin with we establish a class of upper bounds over the achievable entanglementbetween the reference site and various vertices. We observe that the maximum of theseupper bounds is one e-bit. We conclude that the reference site can generate a Bell statewith a vertex if the corresponding upper bound of the vertex is one e-bit. Thus forgeneration of a Bell state this upper bound must be saturated. Taking this into account, weobtain the characteristic constraint of the proper graphs. We introduce a special class ofantipodal invariant stratification graphs, which is called reflective, whereas the antipodevertex obeys the characteristic constraint. We also show that the antipodal associationscheme graphs are reflective so Bell states can be generated between the antipodalvertices. Moreover, we observe that in such graphs the proper Hamiltonian thatenables the creation of a Bell state is the Heisenberg interaction between vertexpairs.
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