  Diffusion noise represents a major constraint to successful liquid state
nano-NMR spectroscopy. Using the Fisher information as a faithful measure, we
theoretically calculate and experimentally show that phase sensitive protocols
are superior in most experimental scenarios, as they maximize information
extraction from correlations in the sample. We derive the optimal experimental
parameters for quantum heterodyne detection (Qdyne) and present the most
accurate statistically polarized nano-NMR Qdyne detection experiments to date,
leading the way to resolve chemical shifts and $J$ couplings at the nanoscale.
