Detecting identical entanglement pure states for two qubits

Entanglement is one of the most surprising features of composite quantum systems. Yet, challenges remain in our understanding and quantification of the entanglement. There is no unique degree of entanglement from various measures, as presented by numerous studies on quantifying entanglement. As indicated in this paper, any degree of entanglement for two qubits resulting from a particular measure can be detected in excess of one corresponding pure state. Evidently, those identical entanglement pure states can be counted as a quantitative condition to be satisfied by other proper measures. The most popular measures of pure states for two qubits are based on the same structure, as indicated in this paper. Then, the algorithm to detect the identical entanglement pure states for two qubits is proposed based on randomness distillation. Eventually, two sets of identical entanglement states are listed for two qubits.