Locking entanglement measures with a single qubit
Karol Horodecki, Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim
TL;DR
It is proved that any convex and asymptotically noncontinuous measure is lockable, as a consequence, all the convex-roof measures can be locked.
Abstract
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.