Progress towards a unified approach to entanglement distribution

Abstract: Entanglement distribution is key to the success of secure communication schemes based on quantum mechanics, and there is a strong need for an ultimate architecture able to overcome the limitations of recent proposals such as those based on entanglement percolation or quantum repeaters. In this work we provide broad theoretical background for the development of such technologies. In particular, we investigate the question of whether entanglement distribution is more efficient if some amount of entanglement -- or some amount of correlations in general -- is available prior to the transmission stage of the protocol. We show that in the presence of noise the answer to this question strongly depends on the type of noise and on the way how entanglement is quantified. On the one hand, subadditive entanglement measures do not show advantage of preshared correlations if entanglement is established via combinations of single-qubit Pauli channels. On the other hand, based on the superadditivity conjecture of distillable entanglement, we provide evidence that this phenomenon occurs for this measure. These results strongly suggest that sending one half of some pure entangled state down a noisy channel is the best strategy for any subadditive entanglement quantifier, thus paving the way to a unified approach for entanglement distribution which does not depend on the nature of noise. We also provide general bounds for entanglement distribution involving quantum discord, and present a counter-intuitive phenomenon of the advantage of arbitrarily little entangled states over maximally entangled ones, which may also occur for quantum channels relevant in experiments.