  Practical implementations of quantum information-theoretic applications rely
on phase coherences between systems. These coherences are disturbed by
misalignment between phase references. Quantum states carrying phase-asymmetry
act as resources to counteract this misalignment. In this paper, we construct
protocols for interconverting these resources by first estimating the
misalignment. Our method achieves sublinear, but otherwise arbitrarily high,
asymptotic rate of conversion of pure resource states to mixed ones. No other
method is known for asymptotic pure-to-mixed state conversion. Our method also
has the advantage of achieving phase reference alignment in addition to
resource conversion.
