Generating maximally entangled distant pair in invariant stratification spin networks

TL;DR

This paper investigates how to generate maximally entangled Bell states between distant vertices in quantum spin networks using invariant stratification graphs, establishing bounds and conditions for optimal entanglement.

Contribution

It introduces a class of graphs called reflective antipodal invariant stratification graphs and identifies the Heisenberg interaction as key for Bell state generation.

Findings

Maximum achievable entanglement is 1 e-bit.

Bell states can be generated between antipodal vertices.

Proper Hamiltonian is the Heisenberg interaction.

Abstract

In this paper we study the generation of Bell states between distant vertices in a permanently coupled quantum spin network, interacting via invariant stratification graphs. To begin with we establish a class of upper bounds over achievable entanglement between the reference site and various vertices. We observe that the maximum of these upper bounds is 1 e-bit. We conclude that the reference site can generate a Bell state with a vertex if the corresponding upper bound of the vertex is 1 e-bit. Thus for generation of a Bell state this upper bound must be saturated. Taking this into account, we obtain the characteristic constraint of the proper graphs. We introduce a special class of antipodal invariant stratification graphs, which is called reflective, whereas the antipode vertex obeys the characteristic constraint. We also show that the antipodal association scheme graphs are reflective so Bell states can be generated between the antipodal vertices. Moreover we observe that in such graphs the proper Hamiltonian that enables creation of Bell state is the Heisenberg interaction between vertex pairs.