Quantum Cloning in $d$ dimensions

Abstract

The quantum state space $\mathcal{S}$ over a $d$-dimensional Hilbert space is represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset {\mathbf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then associated with the affine transformations of ${\mathbf{R}}^D,$ 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.

8 pages LaTeX, no figures

References in corpus (5)

• Optimal Quantum Cloning Machines
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Optimal universal quantum cloning and state estimation
• Quantum copying: A network

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