Two local observables are sufficient to characterize maximally entangled states of N qubits

Maximally entangled states (MES) represent a valuable resource in quantum information processing. In N-qubit systems the MES are N-GHZ states [i.e., the collection of vertical bar GHZ(N)> = 1/root 2(vertical bar 00 ... 0 > + vertical bar 11 ... 1 >)] and its local unitary (LU) equivalences. While it is well known that such states are uniquely stabilized by N commuting observables, in this article we consider the minimum number of noncommuting observables needed to characterize an N-qubit MES as the unique common eigenstate. Here, we prove, rather surprisingly, that in this general case any N-GHZ state can be uniquely stabilized by only two observables. Thus, for the task of MES certification, only two correlated measurements are required with each party observing the spin of his or her system along one of two directions.