  NOON states, states between two modes of light of the form
$|N,0\rangle+e^{i\phi}|0,N\rangle$ allow for super-resolution interformetry. We
show how NOON states can be efficiently produced in circuit quntum
electrodynamics using superconducting phase qubits and resonators. We propose a
protocol where only one interaction between the two modes is required, creating
all the necessary entanglement at the start of the procedure. This protocol
makes active use of the first three states of the phase qubits. Additionally,
we show how to efficiently verify the success of such an experiment, even for
large NOON states, using randomly sampled measurements and semidefinite
programming techniques.
