An Extension of Entanglement Measures for Pure States

To quantify the entanglement is one of the most important topics in quantum entanglement theory. An entanglement measure is built from measures for pure states. Conditions when the entanglement measure is entanglement monotone and convex are presented, as well as the interpretation of smoothed one-shot entanglement cost. Next, a difference between the measure under the local operation and classical communication and the separability-preserving operations is presented. Then, the relation between the convex roof extended method and the way here for the entanglement measures built from the geometric entanglement measure for pure states, as well as the concurrence for pure states in two-qubit systems are considered. It is also shown that the measure is monogamous for 2 circle times 2 circle times d system.