dorsal/arxiv
View SchemaThe Existence of Quantum Entanglement Catalysts
| Authors | Xiaoming Sun, Runyao Duan, Mingsheng Ying |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0311133 |
| URL | https://arxiv.org/abs/quant-ph/0311133 |
| Journal | IEEE. Trans. Inform. Theory, Vol. 51, No. 1, January 2005 |
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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"abstract": "Without additional resources, it is often impossible to transform one\nentangled quantum state into another with local quantum operations and\nclassical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)]\npresented an interesting example showing that the presence of another state,\ncalled a catalyst, enables such a transformation without changing the catalyst.\nThey also pointed out that in general it is very hard to find an analytical\ncondition under which a catalyst exists. In this paper we study the existence\nof catalysts for two incomparable quantum states. For the simplest case of\n$2\\times 2$ catalysts for transformations from one $4\\times 4$ state to\nanother, a necessary and sufficient condition for existence is found. For the\ngeneral case, we give an efficient polynomial time algorithm to decide whether\na $k\\times k$ catalyst exists for two $n\\times n$ incomparable states, where\n$k$ is treated as a constant.",
"arxiv_id": "quant-ph/0311133",
"authors": [
"Xiaoming Sun",
"Runyao Duan",
"Mingsheng Ying"
],
"categories": [
"quant-ph"
],
"journal_ref": "IEEE. Trans. Inform. Theory, Vol. 51, No. 1, January 2005",
"title": "The Existence of Quantum Entanglement Catalysts",
"url": "https://arxiv.org/abs/quant-ph/0311133"
},
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