Institute of Fundamental Technological Research

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a
distinguished basis, whereas the resource theory of purity studies all deviations from the maximally
mixed state. We establish a direct connection between the two resource theories, by identifying purity as the maximal coherence which is achievable by unitary operations. The states that saturate this
maximum identify a universal family of maximally coherent mixed states. These states are optimal
resources under maximally incoherent operations, and thus independent of the way coherence is quantified. For all distance-based coherence quantifiers the maximal coherence can be evaluated exactly, and is shown to coincide with the corresponding distance-based purity quantifier. We further show that purity bounds the maximal amount of entanglement and discord that can be generated by unitary operations, thus demonstrating that purity is the most elementary resource for quantum information processing.

quantum coherence, quantum entanglement, esource theories