Fidelity threshold for long-range entanglement in quantum networks

TL;DR

This paper proposes a method for establishing long-range entanglement in noisy 3D quantum networks, showing that above a certain fidelity threshold, arbitrarily distant qubits can be entangled with constant resources.

Contribution

It introduces a fidelity threshold condition for long-range entanglement in 3D quantum networks, extending previous protocols to higher dimensions and noisy conditions.

Findings

Entanglement can be generated over arbitrary distances if bond fidelity exceeds a critical value.

The protocol works independently of system size, enabling scalable quantum communication.

Constant local resources suffice for long-distance entanglement in noisy 3D networks.

Abstract

We present a strategy to generate long-range entanglement in noisy quantum networks. We consider a cubic lattice whose bonds are partially entangled mixed states of two qubits, and where quantum operations can be applied perfectly at the nodes. In contrast to protocols designed for one- or two-dimensional regular lattices, we find that entanglement can be created between arbitrarily distant qubits if the fidelity of the bonds is higher than a critical value, independent of the system size. Therefore, we show that a constant overhead of local resources, together with connections of finite fidelity, is sufficient to achieve long-distance quantum communication in noisy networks.