Fig. 1: Mixed-state entanglement distribution.
From: A counter-intuitive low entanglement percolation threshold in mixed-state quantum networks
We define and apply mixed-state concurrence percolation to three network topologies, treating the boundaries as two “mega nodes"-the source (S) and target (T): (a) the Bethe lattice (S: the root; T: the outermost layer nodes); (b) the 2D square lattice (S: left boundary; T: right boundary); and (c) the 2D honeycomb lattice (S: left boundary; T: right boundary). In the framework of concurrence percolation, the distribution of entangled mixed states ρ(F) employs a combination of (d) series, (e) parallel, and (f) higher-order connectivity rules to systematically compute the distributable entanglement (concurrence) “sponge-crossing” between S and T. The series and parallel rules can be achieved by quantum operations, specifically (d) entanglement swapping and (e) purification protocols. The two rules can also be used to (f) effectively approximate higher-order connectivity rules which represent unknown quantum operations12.
