Muzaffar Q. Lone, Sudhakar Yarlagadda
We study maximal bipartite entanglement in valence-bond (VB) states and show that the average bipartite entanglement $E_v^2$, between a sub-system of two spins and the rest of the system, can be maximized through a homogenized superposition of the VB states. Our derived maximal $E_v^2$ rapidly increases with system size and saturates at its maximum allowed value. We adopt two ways of generating maximal $E_v^2$ states: (i) starting with a general superposition of VB states, we impose homogeneity; (ii) by considering a general homogeneous state, we generate isotropy. By using these two approaches, we construct explicitly four-qubit and six-qubit highly entangled states that are both isotropic and homogeneous. We also demonstrate that our maximal $E^2_v$ states are ground states of an isotropic infinite range Heisenberg model (IIRHM) and represent a new class of resonating-valence-bond (RVB) states.
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http://arxiv.org/abs/1205.5667
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