Entropic methodology for entanglement measures

Quantifying Entanglement is the key ingredient for the upcoming quantum information technology. Entanglement is hard to grasp, however, which brings about incomplete, indirect ways in proposed measures. Here we show that entropy, as the preferred mathematical quantity to express uncertainty in information theory, can be used to directly detect the entanglement from an arbitrary quantum state. Entanglement is defined as the difference of entropy between the state of system and its corresponding separable state with the same local properties. Remarkably, this general framework is a universal measure of entanglement applies to pure, multipartite, and mixed state. Furthermore, we introduce the disentanglement to find the corresponding separable state for bipartite systems, and give its generalization, called partial disentanglement, for multipartite systems, which breaks the barrier that only concerns the overall entanglement of quantum system, and then concerns the entanglement of a subsystem in composite system and the entanglement between subsystems. Besides, we show that our general framework satisfies the requirements of a proper measures of entanglement.