Quantifying entanglement in terms of an operational way*

We establish entanglement monotones in terms of an operational approach, which is closely connected with the state conversion from pure states to the objective state by the local operations and classical communications. It is shown that any good entanglement quantifier defined on pure states can induce an entanglement monotone for all density matrices. Particularly, we show that our entanglement monotone is the maximal one among all those having the same form for pure states. In some special cases, our proposed entanglement monotones turn to be equivalent to the convex roof construction, which hence gain an operational meaning. Some examples are given to demonstrate different cases.

Automated summary

We establish entanglement monotones in terms of an operational approach, showing that any good entanglement quantifier defined on pure states can induce an entanglement monotone for all density matrices, with our proposed monotone being the maximum among those with the same form in pure states. In certain special cases, our proposed entanglement monotones are equivalent to the convex roof construction, giving them an operational meaning.