dorsal/arxiv
View SchemaQuantum Cloning in $d$ dimensions
| Authors | Paolo Zanardi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9804011 |
| URL | https://arxiv.org/abs/quant-ph/9804011 |
| DOI | 10.1103/PhysRevA.58.3484 |
| Journal | Phys.Rev. A58 (1998) 3484 |
Abstract
The quantum state space $\cal S$ over a $d$-dimensional Hilbert space is represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset {\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then associated with the affine transformations of ${\bf{R}}^D,$ and $N\mapsto M$ {\it cloners} induce polynomial mappings. In this geometrical setting it is shown that an optimal cloner can be chosen covariant and induces a map between reduced density matrices given by a simple contraction of the associated $D$-dimensional Bloch vectors.
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"abstract": "The quantum state space $\\cal S$ over a $d$-dimensional Hilbert space is\nrepresented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\\subset\n{\\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then\nassociated with the affine transformations of ${\\bf{R}}^D,$ and $N\\mapsto M$\n{\\it cloners} induce polynomial mappings. In this geometrical setting it is\nshown that an optimal cloner can be chosen covariant and induces a map between\nreduced density matrices given by a simple contraction of the associated\n$D$-dimensional Bloch vectors.",
"arxiv_id": "quant-ph/9804011",
"authors": [
"Paolo Zanardi"
],
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"quant-ph"
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"doi": "10.1103/PhysRevA.58.3484",
"journal_ref": "Phys.Rev. A58 (1998) 3484",
"title": "Quantum Cloning in $d$ dimensions",
"url": "https://arxiv.org/abs/quant-ph/9804011"
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