  Quantum instruments derived from composite systems allow greater measurement
precision than their classical counterparts due to coherences maintained
between N components; spins, atoms or photons. Decoherence that plagues
real-world devices can be particle loss, or thermal excitation and relaxation,
or dephasing due to external noise sources -- and also due to prior parameter
uncertainty. All these adversely affect precision estimation of time, phase or
frequency. We develop a novel technique uncovering the uniquely optimal probe
states of the N `qubits' alongside new tight bounds on precision under local
and collective mechanisms of these noise types above. For large quantum
ensembles where numerical techniques fail, the problem reduces by analogy to
finding the ground state of a 1-D particle in a potential well; the shape of
the well is dictated by the type and strength of decoherence. The formalism is
applied to prototypical Mach-Zehnder and Ramsey interferometers to discover the
ultimate performance of real-world instruments.
