Locking entanglement with a single qubit.
We study the loss of entanglement of a bipartite state subjected to discarding or measurement of one qubit. Examining behavior of different entanglement measures, we find that entanglement of formation, entanglement cost, logarithmic negativity, and one-way distillable entanglement are lockable measures in that they can decrease arbitrarily after measuring one qubit. We prove that any convex and asymptotically noncontinuous measure is lockable. As a consequence, all the convex-roof measures can be locked. The relative entropy of entanglement is shown to be a nonlockable measure.
Horodecki
Karol
K
Department of Mathematics Physics and Computer Science, University of Gdańsk, 80-952 Gdańsk, Poland.
Horodecki
Michał
M
Horodecki
Paweł
P
Oppenheim
Jonathan
J