  Entanglement is one of the key resources required for quantum computation, so
experimentally creating and measuring entangled states is of crucial importance
in the various physical implementations of a quantum computer. In
superconducting qubits, two-qubit entangled states have been demonstrated and
used to show violations of Bell's Inequality and to implement simple quantum
algorithms. Unlike the two-qubit case, however, where all maximally-entangled
two-qubit states are equivalent up to local changes of basis, three qubits can
be entangled in two fundamentally different ways, typified by the states
$|\mathrm{GHZ}> = (|000> + |111>)/\sqrt{2}$ and $|\mathrm{W}> = (|001> + |010>
+ |100>)/\sqrt{3}$. Here we demonstrate the operation of three coupled
superconducting phase qubits and use them to create and measure
$|\mathrm{GHZ}>$ and $|\mathrm{W}>$ states. The states are fully characterized
using quantum state tomography and are shown to satisfy entanglement witnesses,
confirming that they are indeed examples of three-qubit entanglement and are
not separable into mixtures of two-qubit entanglement.
