Topological conditions for scalable series-parallel percolation

Establish topological conditions under which general uniform scalable series-parallel quantum networks are guaranteed to achieve entanglement percolation during infinite expansion.

Background

The paper develops asymptotic criteria for particular series and parallel-then-series architectures, including conditions involving products of link entanglements and network width. These results do not yield a general topological characterization for all uniformly scalable series-parallel quantum networks.

A universal topological criterion would clarify which network expansions preserve nonzero long-range entanglement independently of the specific reduction sequence.