  We introduce the $q$-potential as an extension of the Benedetto-Fickus frame
potential, defined on general reconstruction systems and we show that protocols
are the minimizers of this potential under certain restrictions. We extend
recent results of B.G. Bodmann on the structure of optimal protocols with
respect to 1 and 2 lost packets where the worst (normalized) reconstruction
error is computed with respect to a compatible unitarily invariant norm. We
finally describe necessary and sufficient (spectral) conditions, that we call
$q$-fundamental inequalities, for the existence of protocols with prescribed
properties by relating this problem to Klyachko's and Fulton's theory on sums
of hermitian operators.
