Deterministic Entanglement Distribution on Series-Parallel Quantum
  Networks
The performance of distributing entanglement between two distant nodes in a
large-scale quantum network (QN) of partially entangled bipartite pure states
is generally benchmarked against the classical entanglement percolation (CEP)
scheme. Improvements beyond CEP were only achieved by nonscalable strategies
for restricted QN topologies. This paper explores and amplifies a new and more
effective mapping of a QN, referred to as concurrence percolation theory
(ConPT), that suggests using deterministic rather than probabilistic protocols
for scalably improving on CEP across arbitrary QN topologies. More precisely,
we implement ConPT via a deterministic entanglement transmission (DET) scheme
that is fully analogous to resistor network analysis, with the corresponding
series and parallel rules represented by deterministic entanglement swapping
and concentration protocols, respectively. The main contribution of this paper
is to establish a powerful mathematical framework, which is applicable to
arbitrary d-dimensional information carriers (qudits), that provides different
natural optimality metrics in terms of generalized k-concurrences (a family of
fundamental entanglement measures) for different QN topology. In particular, we
conclude that the introduced DET scheme (a) is optimal over the well-known
nested repeater protocol for distilling entanglement from partially entangled
qubits and (b) leads to higher success probabilities of obtaining a maximally
entangled state than using CEP. The implementation of the DET scheme is
experimentally feasible as tested on IBM's quantum computation platform.
Xiangyi Meng Yulong Cui Jianxi Gao Shlomo Havlin Andrei E. Ruckenstein