Shane KELLY
We investigate the dynamics of the relative entropy of coherence in random hybrid circuits and its role in the protection of quantum information. We first develop a Markovian theory of coherence to predict and control entanglement transitions. We then investigate the purification dynamics, and show that the coherence free limit of such circuits provide an example of a classical error correction transition in which the classical channel capacity acts as an order parameter. This allows us to distinguish the quantum features of the previously studied quantum purification transitions as the ability to protect against dephasing errors and an extensive scaling of coherence in all local basises. Using this intuition we conclude by proving that the coherence in any local basis gives an upper bound for the quantum code distance of any stabilizer quantum error correction code. Such a bound provides a rigorous quantification of the coherence resource requirements for quantum error correction.