  Quantum asymmetry is a physical resource which coincides with the amount of
coherence between the eigenspaces of a generator responsible for phase encoding
in interferometric experiments. We highlight an apparently counter-intuitive
behavior that the asymmetry may \emph{increase} as a result of a
\emph{decrease} of coherence inside a degenerate subspace. We intuitively
explain and illustrate the phenomena by performing a three-mode single-photon
interferometric experiment, where one arm carries the signal and two noisy
reference arms have fluctuating phases. We show that the source of the observed
sensitivity improvement is the reduction of correlations between these
fluctuations and comment on the impact of the effect when moving from the
single-photon quantum level to the classical regime. Finally, we also establish
the analogy of the effect in the case of entanglement resource theory.
