dorsal/arxiv
View SchemaLinearly-independent quantum states can be cloned
| Authors | Lu-Ming Duan, Guang-Can Guo |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9705018 |
| URL | https://arxiv.org/abs/quant-ph/9705018 |
Abstract
A fundamental question in quantum mechanics is, whether it is possible to replicate an arbitrary unknown quantum state. Then famous quantum no-cloning theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open the following question: If the state is not arbitrary, but secretly chosen from a certain set $\$={ | \Psi _1> ,| \Psi_2> ,... ,| \Psi _n> } $, whether is the cloning possible? This question is of great practical significance because of its applications in quantum information theory. If the states $| \Psi_1>, | \Psi_2>,...$ and $| \Psi_n> $ are linearly-dependent, similar to the proof of the no-cloning theorem, the linearity of quantum mechanics forbids such replication. In this paper, we show that, if the states $| \Psi_1>, | \Psi _2>, ...$ and $| \Psi_n> $ are linearly-independent, they do can be cloned by a unitary-reduction process.
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"abstract": "A fundamental question in quantum mechanics is, whether it is possible to\nreplicate an arbitrary unknown quantum state. Then famous quantum no-cloning\ntheorem [Nature 299, 802 (1982)] says no to the question. But it leaves open\nthe following question: If the state is not arbitrary, but secretly chosen from\na certain set $\\$={ | \\Psi _1\u003e ,| \\Psi_2\u003e ,... ,| \\Psi _n\u003e } $, whether is the\ncloning possible? This question is of great practical significance because of\nits applications in quantum information theory. If the states $| \\Psi_1\u003e, |\n\\Psi_2\u003e,...$ and $| \\Psi_n\u003e $ are linearly-dependent, similar to the proof of\nthe no-cloning theorem, the linearity of quantum mechanics forbids such\nreplication. In this paper, we show that, if the states $| \\Psi_1\u003e, | \\Psi _2\u003e,\n...$ and $| \\Psi_n\u003e $ are linearly-independent, they do can be cloned by a\nunitary-reduction process.",
"arxiv_id": "quant-ph/9705018",
"authors": [
"Lu-Ming Duan",
"Guang-Can Guo"
],
"categories": [
"quant-ph"
],
"title": "Linearly-independent quantum states can be cloned",
"url": "https://arxiv.org/abs/quant-ph/9705018"
},
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