Quantifying the entanglement of quantum states under the geometry method

Abstract

Quantifying entanglement is an important issue in quantum information theory. A straightforward method to quantify entanglement is to measure the distance between the entangled state and the separable sets under the fidelity, distance norm and so on. However, there are few results on the entanglement measure in terms of trace norm. Here we consider the entanglement measures through the trace norm in terms of three methods, the standard measure, the modified measure and the way proposed in [Phys. Rev. A 102. 062401 ( 2020)]. Specifically, we present some properties of the entanglement measures under the three methods. We also present the analytical expressions for a class of mixed states on two-qubit systems for the standard measure, the pure states for the modified measure and the mixed states on two-qubit systems for the method generated under the third way. And we also generalize the bipartite entanglement measure to a measure for the tripartite states.