Optimally preserving quantum correlations and coherence with eternally non-Markovian dynamics

We demonstrate, both analytically and experimentally, the usefulness of non-Markovianity for preserving correlations and coherence in quantum systems. For this, we consider a broad class of qubit evolutions, having a decoherence matrix separated from zero for large times. While any such Markovian evolution leads to an exponential loss of correlations, non-Markovianity can help to preserve correlations even in the limit t → ∞. In fact, under general assumptions, eternally non-Markovian evolution naturally emerges as the one that allows for optimal preservation of quantum correlations. For covariant qubit evolutions, we also show that non-Markovianity can be used to preserve quantum coherence at all times, which is an important resource for quantum metrology. We explicitly demonstrate this effect experimentally with linear optics, by implementing the optimal non-Markovian quantum evolution.