  Vast developments in quantum technology have enabled the preparation of
quantum states with more than a dozen entangled qubits. The full
characterization of such systems demands distinct constructions depending on
their specific type and the purpose of their use. Here we present a method that
scales linearly with the number of qubits for characterizing stabilizer states.
Our approach allows simultaneous extraction of information about the fidelity,
the entanglement, and the nonlocality of the state and thus is of high
practical relevance. We demonstrate the efficient applicability of our method
by performing an experimental characterization of a photonic four-qubit cluster
state and three- and four-qubit Greenberger-Horne-Zeilinger states. Our scheme
can be directly extended to larger-scale quantum information tasks.
