  Tight frames and rank-one quantum measurements are shown to be intimately
related. In fact, the family of normalized tight frames for the space in which
a quantum mechanical system lies is precisely the family of rank-one
generalized quantum measurements (POVMs) on that space. Using this
relationship, frame-theoretical analogues of various quantum-mechanical
concepts and results are developed.
  The analogue of a least-squares quantum measurement is a tight frame that is
closest in a least-squares sense to a given set of vectors. The least-squares
tight frame is found for both the case in which the scaling of the frame is
specified (constrained least-squares frame (CLSF)) and the case in which the
scaling is free (unconstrained least-squares frame (ULSF)). The well-known
canonical frame is shown to be proportional to the ULSF and to coincide with
the CLSF with a certain scaling.
  Finally, the canonical frame vectors corresponding to a geometrically uniform
vector set are shown to be geometrically uniform and to have the same
symmetries as the original vector set.
