The role of local and global geometry in quantum entanglement percolation (1311.6706v2)

Abstract: We prove that enhanced entanglement percolation via lattice transformation is possible even if the new lattice is more poorly connected in that: i) the coordination number (a local property) decreases, or ii) the classical percolation threshold (a global property) increases. In searching for protocols to transport entanglement across a network, it seems reasonable to try transformations that increase connectivity. In fact, all examples that we are aware of violate both conditions i and ii. One might therefore conjecture that all good transformations must violate them. Here we provide a counter-example that satisfies both conditions by introducing a new method, partial entanglement swapping. This result shows that a transformation may not be rejected on the basis of satisfying conditions i or ii. Both the result and the new method constitute steps toward answering basic questions, such as whether there is a minimum amount of local entanglement required to achieve long-range entanglement.