# A set of $4d-3$ observables to determine any pure qudit state. (arXiv:1903.05709v1 [quant-ph])

We present a tomographic method which requires only $4d-3$ measurement
outcomes to reconstruct \emph{any} pure quantum state of arbitrary dimension
$d$. Using the proposed scheme we have experimentally reconstructed a large
number of pure states of dimension $d=7$, obtaining a mean fidelity of $0.94$.
Moreover, we performed numerical simulations of the reconstruction process,
verifying the feasibility of the method for higher dimensions. In addition, the
\emph{a priori} assumption of purity can be certified within the same set of
measurements, what represents an improvement with respect to other similar
methods and contributes to answer the question of how many observables are
needed to uniquely determine any pure state.