  We introduce for SU(2) quantum spin systems the Valence Bond Entanglement
Entropy as a counting of valence bond spin singlets shared by two subsystems.
For a large class of antiferromagnetic systems, it can be calculated in all
dimensions with Quantum Monte Carlo simulations in the valence bond basis. We
show numerically that this quantity displays all features of the von Neumann
entanglement entropy for several one-dimensional systems. For two-dimensional
Heisenberg models, we find a strict area law for a Valence Bond Solid state and
multiplicative logarithmic corrections for the Neel phase.
