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Optimal estimation of quantum dynamics

A. Acin·E. Jane·G. Vidal
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Abstract

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.

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A. Acin, E. Jane, G. Vidal. 2000-12-04. Optimal estimation of quantum dynamics. https://doi.org/10.1103/physreva.64.050302

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