  Frustration in quantum many body systems is quantified by the degree of
incompatibility between the local and global orders associated, respectively,
to the ground states of the local interaction terms and the global ground state
of the total many-body Hamiltonian. This universal measure is bounded from
below by the ground-state bipartite block entanglement. For many-body
Hamiltonians that are sums of two-body interaction terms, a further inequality
relates quantum frustration to the pairwise entanglement between the
constituents of the local interaction terms. This additional bound is a
consequence of the limits imposed by monogamy on entanglement shareability. We
investigate the behavior of local pair frustration in quantum spin models with
competing interactions on different length scales and show that valence bond
solids associated to exact ground-state dimerization correspond to a transition
from generic frustration, i.e. geometric, common to classical and quantum
systems alike, to genuine quantum frustration, i.e. solely due to the
non-commutativity of the different local interaction terms. We discuss how such
frustration transitions separating genuinely quantum orders from classical-like
ones are detected by observable quantities such as the static structure factor
and the interferometric visibility.
