Long-distance entanglement generation in two-dimensional networks

Abstract

We consider 2D networks composed of nodes initially linked by two-qubit mixed states. In these networks we develop a global error correction scheme that can generate distance-independent entanglement from arbitrary network geometries using rank two states. By using this method and combining it with the concept of percolation we also show that the generation of long distance entanglement is possible with rank three states. Entanglement percolation and global error correction have different advantages depending on the given situation. To reveal the trade-off between them we consider their application on networks containing pure states. In doing so we find a range of pure-state schemes, each of which has applications in particular circumstances: For instance, we can identify a protocol for creating perfect entanglement between two distant nodes. However, this protocol can not generate a singlet between any two nodes. On the other hand, we can also construct schemes for creating entanglement between any nodes, but the corresponding entanglement fidelity is lower.

Distribution of entanglement in large-scale quantum networks

“…Protocols on networks using this approach were studied in [24,25]. This work was extended to a hybrid approach addressing both the first and second question in [81]. The protocols presented in these three articles are the subject of this subsection.…”

“…In the case where the parameters are different within a link, we must first do a PCM, which maps the problem to the original pure-state percolation problem with some of the links probabilistically deleted. A similar idea is used in [81], where pairs in certain rank-three states replace the PMSs. These can be converted to binary states via a sort of PCM that leave a separable state on failure.…”

Limited-path-length entanglement percolation in quantum complex networks

“…The probability η The function generating ξ(s, t) can be computed similar to Eqs. (12) and (14). In this case, it is a function of two variables: h ξ (x, y) = s,t≥0 ξ(s, t)y s x t .…”

“…In this case, a higher number of paths may exist which can help in the communication: with the existence of clusters of nodes connected by entangled states, two distant nodes will be able to establish entanglement between them if they both belong to the same cluster [4]. Entanglement percolation, which makes use of such higher dimensional networks, was first proposed in the honeycomb lattice [5] and later extended to other regular lattices [6,7], to schemes using multipartite entanglement [8] and to noisy networks [9][10][11][12]. In Ref.…”

Nonlocal dissipative tunneling for high-fidelity quantum-state transfer between distant parties

“…Much of the recent research in the quantum information field has focused on developing new techniques to engineer long-distance entanglement [1][2][3][4] and to obtain high-fidelity communication between distant parties [5][6][7][8]. Mastery of these techniques represents a crucial step toward the practical implementation of quantum computing and communication protocols, and developments have been witnessed within both bosonic and fermionic systems.…”