  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.
