Physics – Quantum Physics
Scientific paper
2003-11-19
IEEE. Trans. Inform. Theory, Vol. 51, No. 1, January 2005
Physics
Quantum Physics
12 pages. Presentation part improved. Main results unchanged. Essentially the journal version
Scientific paper
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. 83, 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 $2\times 2$ catalysts for transformations from one $4\times 4$ 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 $k\times k$ catalyst exists for two $n\times n$ incomparable states, where $k$ is treated as a constant.
Duan Runyao
Sun Xiaoming
Ying Mingsheng
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