Toolbox for entanglement detection and fidelity estimation

The determination of the state fidelity and the detection of entanglement are fundamental problems in quantum information experiments. We investigate how these goals can be achieved with a minimal effort. We show that the fidelity of Greenberger-Horne-Zeilinger and $W$ states can be determined with an effort increasing only linearly with the number of qubits. We also present simple and robust methods for other states, such as cluster states and states in decoherence-free subspaces.