dorsal/arxiv
View SchemaEconomical quantum cloning in any dimension
| Authors | Thomas Durt, Jaromir Fiurasek, Nicolas J. Cerf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412201 |
| URL | https://arxiv.org/abs/quant-ph/0412201 |
| DOI | 10.1103/PhysRevA.72.052322 |
| Journal | Phys. Rev. A 72, 052322 (2005). |
Abstract
The possibility of cloning a d-dimensional quantum system without an ancilla is explored, extending on the economical phase-covariant cloning machine found in [Phys. Rev. A {\bf 60}, 2764 (1999)] for qubits. We prove the impossibility of constructing an economical version of the optimal universal cloning machine in any dimension. We also show, using an ansatz on the generic form of cloning machines, that the d-dimensional phase-covariant cloner, which optimally clones all uniform superpositions, can be realized economically only in dimension d=2. The used ansatz is supported by numerical evidence up to d=7. An economical phase-covariant cloner can nevertheless be constructed for d>2, albeit with a lower fidelity than that of the optimal cloner requiring an ancilla. Finally, using again an ansatz on cloning machines, we show that an economical version of the Fourier-covariant cloner, which optimally clones the computational basis and its Fourier transform, is also possible only in dimension d=2.
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"abstract": "The possibility of cloning a d-dimensional quantum system without an ancilla\nis explored, extending on the economical phase-covariant cloning machine found\nin [Phys. Rev. A {\\bf 60}, 2764 (1999)] for qubits. We prove the impossibility\nof constructing an economical version of the optimal universal cloning machine\nin any dimension. We also show, using an ansatz on the generic form of cloning\nmachines, that the d-dimensional phase-covariant cloner, which optimally clones\nall uniform superpositions, can be realized economically only in dimension d=2.\nThe used ansatz is supported by numerical evidence up to d=7. An economical\nphase-covariant cloner can nevertheless be constructed for d\u003e2, albeit with a\nlower fidelity than that of the optimal cloner requiring an ancilla. Finally,\nusing again an ansatz on cloning machines, we show that an economical version\nof the Fourier-covariant cloner, which optimally clones the computational basis\nand its Fourier transform, is also possible only in dimension d=2.",
"arxiv_id": "quant-ph/0412201",
"authors": [
"Thomas Durt",
"Jaromir Fiurasek",
"Nicolas J. Cerf"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.72.052322",
"journal_ref": "Phys. Rev. A 72, 052322 (2005).",
"title": "Economical quantum cloning in any dimension",
"url": "https://arxiv.org/abs/quant-ph/0412201"
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