  We study the loss of entanglement of bipartite state subjected to discarding
or measurement of one qubit. Examining the behavior of different entanglement
measures, we find that entanglement of formation, entanglement cost, and
logarithmic negativity are lockable measures in that it can decrease
arbitrarily after measuring one qubit. We prove that any convex and
asymptotically non-continuous measure is lockable. As a consequence, all the
convex roof measures can be locked. Relative entropy of entanglement is shown
to be a non-lockable measure.
