An Extension of Entanglement Measures for Pure States

Abstract

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⊗2⊗d system.

Quantifying the entanglement of quantum states under the geometry method

“…Then we present the modified entanglement measure based on the trace norm of a class of entangled states, we also present some properties of the modified measure. At last, we consider the distance measure on the trace norm under the method presented in [24,25], we present this measure is monogamous for n-qubit systems .…”

“…Due to the results in [24], we know that the above quantity is an entanglement measure, that is, [27], by the results in [25], we have the following corollary,…”

“…Here we consider another entanglement measure based on the trace norm under the method presented in [24,25]. There the authors presented a way to generate the entanglement measure E for the mixed states from the entanglement measure E on pure states.…”

“…We also present that the modified measure satisfies the similar properties with the standard one. In the third section, we consider the measure under the trace norm under the method proposed in [24,25]. In section IV, we end with a conclusion.…”

A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

“…[6] The other interesting approach with operational significance to quantify the entanglement is proposed in refs. [7,8]. Compared with the bipartite entanglement systems, the complexity of a multipartite entanglement system grows remarkably with the increasing number of parties and the increasing dimension of the systems.…”