  We present a null witness of the dimension of a quantum system,
discriminating real, complex and classical spaces, based on equality due to
linear independence. The witness involves only a single measurement with
sufficiently many outcomes and prepared input states. In addition, for
intermediate dimensions, the witness bounds saturate for a family of
equiangular tight frames including symmetric informationally complete positive
operator valued measures. Such a witness requires a minimum of resources, being
robust against many practical imperfections. We also discuss errors due to
finite statistics.
