dorsal/arxiv
View SchemaOptical Quantum Cloning - a Review
| Authors | Nicolas J. Cerf, Jaromir Fiurasek |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0512172 |
| URL | https://arxiv.org/abs/quant-ph/0512172 |
| Journal | Progress in Optics, vol. 49, Edt. E. Wolf (Elsevier, 2006), p. 455. |
Abstract
After a brief introduction to the quantum no-cloning theorem and its link with the linearity and causality of quantum mechanics, the concept of quantum cloning machines is sketched, following, whenever possible, the chronology of the main results. The important classes of quantum cloning machines are reviewed, in particular state-independent and state-dependent cloning machines. The 1-to-2 cloning problem is then studied from a formal point of view, using the isomorphism between completely positive maps and operators, which leads to the so-called double-Bell ansatz. This also yields an efficient numerical approach to quantum cloning, based on semidefinite programming methods. The derivation of the optimal N-to-M universal cloning machine in d dimensions is then detailed, as well as the notion of asymmetric cloning machines. In the second part of this review, the optical implementation of cloning machines is considered. It is shown that the universal cloning of photons can be achieved by parametric amplification of light or by symmetrization via the Hong-Ou-Mandel effect. The various experimental demonstrations of quantum cloning machines are reviewed. The cloning of orthogonally polarized photons is also considered, as well as the asymmetric and phase-covariant cloning of photons. Finally, the extension of quantum cloning to continuous variables is analyzed. The optimal cloning of coherent states of light by phase-insensitive amplification is explained, as well as the experimental realization of continuous-variable quantum cloning with linear optics, measurement, and feed-forward operations.
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"abstract": "After a brief introduction to the quantum no-cloning theorem and its link\nwith the linearity and causality of quantum mechanics, the concept of quantum\ncloning machines is sketched, following, whenever possible, the chronology of\nthe main results. The important classes of quantum cloning machines are\nreviewed, in particular state-independent and state-dependent cloning machines.\nThe 1-to-2 cloning problem is then studied from a formal point of view, using\nthe isomorphism between completely positive maps and operators, which leads to\nthe so-called double-Bell ansatz. This also yields an efficient numerical\napproach to quantum cloning, based on semidefinite programming methods. The\nderivation of the optimal N-to-M universal cloning machine in d dimensions is\nthen detailed, as well as the notion of asymmetric cloning machines. In the\nsecond part of this review, the optical implementation of cloning machines is\nconsidered. It is shown that the universal cloning of photons can be achieved\nby parametric amplification of light or by symmetrization via the\nHong-Ou-Mandel effect. The various experimental demonstrations of quantum\ncloning machines are reviewed. The cloning of orthogonally polarized photons is\nalso considered, as well as the asymmetric and phase-covariant cloning of\nphotons. Finally, the extension of quantum cloning to continuous variables is\nanalyzed. The optimal cloning of coherent states of light by phase-insensitive\namplification is explained, as well as the experimental realization of\ncontinuous-variable quantum cloning with linear optics, measurement, and\nfeed-forward operations.",
"arxiv_id": "quant-ph/0512172",
"authors": [
"Nicolas J. Cerf",
"Jaromir Fiurasek"
],
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],
"journal_ref": "Progress in Optics, vol. 49, Edt. E. Wolf (Elsevier, 2006), p.\n 455.",
"title": "Optical Quantum Cloning - a Review",
"url": "https://arxiv.org/abs/quant-ph/0512172"
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