  Atomic (qubit) and optical or microwave (modal) phase-estimation protocols
are placed on the same footing in terms of quantum-circuit diagrams. Circuit
equivalences are used to demonstrate the equivalence of protocols that achieve
the Heisenberg limit by employing entangled superpositions of Fock states, such
as N00N states. The key equivalences are those that disentangle a circuit so
that phase information is written exclusively on a mode or modes or on a qubit.
The Fock-state-superposition phase-estimation circuits are converted to use
entangled coherent-state superpositions; the resulting protocols are more
amenable to realization in the lab, particularly in a qubit/cavity setting at
microwave frequencies.
