  Localizability of entanglement in fully inseparable states is a key
ingredient of assisted quantum information protocols as well as
measurement-based models of quantum computing. We investigate the existence of
fully inseparable states with nonlocalizable entanglement, that is, with
entanglement which cannot be localized between any pair of subsystems by any
measurement on the remaining part of the system. It is shown, that the
nonlocalizable entanglement occurs already in suitable mixtures of a
three-qubit GHZ state and white noise. Further, we generalize this set of
states to a two-parametric family of fully inseparable three-qubit states with
nonlocalizable entanglement. Finally, we demonstrate experimentally the
existence of nonlocalizable entanglement by preparing and characterizing one
state from the family using correlated single photons and linear optical
circuit.
