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.

8 pages; published version