# Noise Effects on Entanglement Distribution by Separable State

## TL;DR

This paper studies how noise impacts the ability to distribute entanglement using separable states in quantum networks, revealing critical noise thresholds and their dependence on system dimensions.

## Contribution

It demonstrates that under various noise models, the average distributed entanglement equals bipartite entanglement in specific partitions, and identifies critical noise levels for entanglement distribution.

## Key findings

- Average distributed entanglement equals bipartite entanglement in certain partitions.
- Existence of a critical noise parameter beyond which entanglement cannot be distilled.
- Critical noise threshold increases with the Hilbert space dimension for d-dimensional Bell states.

## Abstract

We investigate noise effects on the performance of entanglement distribution by separable state. We consider a realistic situation in which the mediating particle between two distant nodes of the network goes through a noisy channel. For a large class of noise models we show that the average value of distributed entanglement between two parties is equal to entanglement between particular bipartite partitions of target qubits and exchange qubit in intermediate steps of the protocol. This result is valid for distributing two qubit/qudit and three qubit entangled states. In explicit examples of the noise family, we show that there exists a critical value of noise parameter beyond which distribution of distillable entanglement is not possible. Furthermore, we determine how this critical value increases in terms of Hilbert space dimension, when distributing $d$-dimensional Bell states.