  We introduce a class of informationally complete positive-operator-valued
measures which are, in analogy with a tight frame, "as close as possible" to
orthonormal bases for the space of quantum states. These measures are
distinguished by an exceptionally simple state-reconstruction formula which
allows "painless" quantum state tomography. Complete sets of mutually unbiased
bases and symmetric informationally complete positive-operator-valued measures
are both members of this class, the latter being the unique minimal rank-one
members. Recast as ensembles of pure quantum states, the rank-one members are
in fact equivalent to weighted 2-designs in complex projective space. These
measures are shown to be optimal for quantum cloning and linear quantum state
tomography.
