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The Existence of Quantum Entanglement Catalysts

Xiaoming Sun·Runyao Duan·Mingsheng Ying
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Abstract

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.

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Xiaoming Sun, Runyao Duan, Mingsheng Ying. 2005-01-18. The Existence of Quantum Entanglement Catalysts. https://arxiv.org/abs/quant-ph/0311133

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