The existence of quantum entanglement catalysts

Without additional resources, it is often impossible to transform one entangled quantum state into another with local quantum operations and classical communication. Jonathan and Plenio (Phys. Rev. Lett., vol. 83, p. 3566, 1999) presented an interesting example showing that the presence of another state, called a catalyst, enables such a transformation without changing the catalyst. They also pointed out that in general it is very hard to find an analytical condition under which a catalyst exists. In this paper, we study the existence of catalysts for two incomparable quantum states. For the simplest case of 2/spl times/2 catalysts for transformations from one 4/spl times/4 state to another, a necessary and sufficient condition for existence is found. For the general case, we give an efficient polynomial time algorithm to decide whether a k/spl times/k catalyst exists for two n/spl times/n incomparable states, where k is treated as a constant.