75,473 research outputs found
The Uniqueness Theorem for Entanglement Measures
We explore and develop the mathematics of the theory of entanglement
measures. After a careful review and analysis of definitions, of preliminary
results, and of connections between conditions on entanglement measures, we
prove a sharpened version of a uniqueness theorem which gives necessary and
sufficient conditions for an entanglement measure to coincide with the reduced
von Neumann entropy on pure states. We also prove several versions of a theorem
on extreme entanglement measures in the case of mixed states. We analyse
properties of the asymptotic regularization of entanglement measures proving,
for example, convexity for the entanglement cost and for the regularized
relative entropy of entanglement.Comment: 22 pages, LaTeX, version accepted by J. Math. Phy
Locking entanglement measures with a single qubit
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.Comment: 5 pages, RevTex
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