  Dynamic correlations of quantum observables are challenging to measure due to
measurement backaction incurred at early times. Recent work [P. Uhrich et al.,
Phys. Rev. A, 96:022127 (2017)] has shown that ancilla-based noninvasive
measurements are able to reduce this backaction, allowing for dynamic
correlations of single-site spin observables to be measured. We generalise this
result to correlations of arbitrary spin observables and extend the measurement
protocol to simultaneous noninvasive measurements which allow for real and
imaginary parts of correlations to be extracted from a single set of
measurements. We use positive operator-valued measures to analyse the dynamics
generated by the ancilla-based measurements. Using this framework we prove that
special observables exist for which measurement backaction is of no concern, so
that dynamic correlations of these can be obtained without making use of
ancillas.
