General entanglement-assisted transformation for bipartite pure quantum states

We introduce the general catalysts for pure entanglement transformations under local operations and classical communications in such a way that we disregard the profit and loss of entanglement of the catalysts per se. As such, the possibilities of pure entanglement transformations are greatly expanded. We also design an efficient algorithm to detect whether a k x k general catalyst exists for a given entanglement transformation. This algorithm can also be exploited to witness the existence of standard catalysts.