  Quantum measurement is universal for quantum computation. Two models for
performing measurement-based quantum computation exist: the one-way quantum
computer was introduced by Briegel and Raussendorf, and quantum computation via
projective measurements only by Nielsen. The more recent development of this
second model is based on state transfers instead of teleportation. From this
development, a finite but approximate quantum universal family of observables
is exhibited, which includes only one two-qubit observable, while others are
one-qubit observables. In this article, an infinite but exact quantum universal
family of observables is proposed, including also only one two-qubit
observable.
  The rest of the paper is dedicated to compare these two models of
measurement-based quantum computation, i.e. one-way quantum computation and
quantum computation via projective measurements only. From this comparison,
which was initiated by Cirac and Verstraete, closer and more natural
connections appear between these two models. These close connections lead to a
unified view of measurement-based quantum computation.
