  It is well known that quantum states that can be transformed into each other
by local unitary transformations are equal from the information theoretic point
of view. This defines equivalence classes of states and allows one to write any
state with the minimal number of parameters called the canonical form of the
state. We define the equivalence classes of local measurements such that local
operations which transform states from one equivalence class into another with
the same probability are equivalent. This equivalence relation allows one to
write the operators with the minimal number of parameters, which we call
canonical operators, and hence the use of the canonical operators simplifies
the optimal manipulation of quantum states. We use the canonical local
operators for the concentration of three-qubit Greenberger-Horne-Zeilinger
states and obtain the optimal concentration protocols in terms of the unitary
invariants of quantum states, namely, the bipartite concurrences and the
three-tangle.
