  The "entanglement cost" of a bipartite measurement is the amount of shared
entanglement two participants need to use up in order to carry out the given
measurement by means of local operations and classical communication. Here we
numerically investigate the entanglement cost of generic orthogonal
measurements on two qubits. Our results strongly suggest that for almost all
measurements of this kind, the entanglement cost is strictly greater than the
average entanglement of the eigenstates associated with the measurements,
implying that the nonseparability of a two-qubit orthogonal measurement is
generically distinct from the nonseparability of its eigenstates.
