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We exploit a ferromagnetic chain of interacting $d$-level ($d>2$) particlesfor arbitrary perfect transfer of quantum states with $(d-1)$ levels. Thepresence of one extra degree of freedom in the Hilbert space of particles,which is not used in encoding, allows to achieve perfect transfer even in auniform chain through a repeated measurement procedure with consecutive singlesite measurements. Apart from the first iteration, for which the time ofevolution grows linearly with the size of the chain, in all other iterations,the evolution times are short and does not scale with the length. The successprobability of the mechanism grows with the number of repetitions andpractically after a few iterations the transfer is accomplished with a highprobability.

Arbitrary perfect state transfer in $d$-level spin chains