Quantum Cloning in $d$ dimensions

Details Quantum Cloning in $d$ dimensions Quantum Cloning in $d$ dimensions

1998-04-03

arxiv.org/abs/quant-ph/9804011v3

Phys.Rev. A58 (1998) 3484

Physics

Quantum Physics

8 pages LaTeX, no figures

Scientific paper

10.1103/PhysRevA.58.3484

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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