Locking entanglement measures with a single qubit

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.

5 pages, RevTex4

References in corpus (12)

• A computable measure of entanglement
• Quantifying Entanglement
• On the volume of the set of mixed entangled states
• Capacities of Quantum Erasure Channels
• Quantum Data Hiding
• Randomizing quantum states: Constructions and applications
• Optimal Encryption of Quantum Bits
• Secure key from bound entanglement
• Continuity of quantum conditional information
• Locking classical correlation in quantum states
• Hiding classical data in multi-partite quantum states
• Classical information and distillable entanglement

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