dorsal/arxiv
View SchemaAsymmetric quantum cloning machines in any dimension
| Authors | Nicolas J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9805024 |
| URL | https://arxiv.org/abs/quant-ph/9805024 |
| DOI | 10.1080/09500340008244036 |
| Journal | J.Mod.Opt. 47 (2000) 187 |
Abstract
A family of asymmetric cloning machines for $N$-dimensional quantum states is introduced. These machines produce two imperfect copies of a single state that emerge from two distinct Heisenberg channels. The tradeoff between the quality of these copies is shown to result from a complementarity akin to Heisenberg uncertainty principle. A no-cloning inequality is derived for isotropic cloners: if $\pi_a$ and $\pi_b$ are the depolarizing fractions associated with the two copies, the domain in $(\sqrt{\pi_a},\sqrt{\pi_b})$-space located inside a particular ellipse representing close-to-perfect cloning is forbidden. More generally, a no-cloning uncertainty relation is discussed, quantifying the impossibility of copying imposed by quantum mechanics. Finally, an asymmetric Pauli cloning machine is defined that makes two approximate copies of a quantum bit, while the input-to-output operation underlying each copy is a (distinct) Pauli channel. The class of symmetric Pauli cloning machines is shown to provide an upper bound on the quantum capacity of the Pauli channel of probabilities $p_x$, $p_y$ and $p_z$.
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"abstract": "A family of asymmetric cloning machines for $N$-dimensional quantum states is\nintroduced. These machines produce two imperfect copies of a single state that\nemerge from two distinct Heisenberg channels. The tradeoff between the quality\nof these copies is shown to result from a complementarity akin to Heisenberg\nuncertainty principle. A no-cloning inequality is derived for isotropic\ncloners: if $\\pi_a$ and $\\pi_b$ are the depolarizing fractions associated with\nthe two copies, the domain in $(\\sqrt{\\pi_a},\\sqrt{\\pi_b})$-space located\ninside a particular ellipse representing close-to-perfect cloning is forbidden.\nMore generally, a no-cloning uncertainty relation is discussed, quantifying the\nimpossibility of copying imposed by quantum mechanics. Finally, an asymmetric\nPauli cloning machine is defined that makes two approximate copies of a quantum\nbit, while the input-to-output operation underlying each copy is a (distinct)\nPauli channel. The class of symmetric Pauli cloning machines is shown to\nprovide an upper bound on the quantum capacity of the Pauli channel of\nprobabilities $p_x$, $p_y$ and $p_z$.",
"arxiv_id": "quant-ph/9805024",
"authors": [
"Nicolas J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340008244036",
"journal_ref": "J.Mod.Opt. 47 (2000) 187",
"title": "Asymmetric quantum cloning machines in any dimension",
"url": "https://arxiv.org/abs/quant-ph/9805024"
},
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