# Entanglement Routing

## Functionality Description

Entanglement routing allows a quantum network to generate long distance entanglement between two or multiple nodes. A Quantum router is a device used to transmit quantum information over long distances along a quantum network using entanglement swapping between routers. As quantum information transmissivity decays exponentially in function of the distance, quantum routers are needed to successfully establish entangled states between any nodes on the quantum network.

There are entanglement routing protocols that are specifically designed for certain network topology e.g: linear, rings, spheres, grids, recursively generated network or for networks with arbitrary topology.

The main goal of entanglement routing is to develop efficient routing protocols to enable long distance entanglement.

## Use Case

• No classical analogue.

## Protocols

Entanglement routing protocol:

Related protocol:

## Properties

• Entanglement routing assumes the presence of:
• Classical and quantum communication physical channels.
• Quantum repeater nodes.
• Quantum repeater nodes:
• Contain qubits that in the short and medium term are applicable to only basic operations i.e, Bell State Measurements to pairs of neighborhood nodes allowing the Entanglement Swapping operation.
• Have global (all the network) or local (just neighborhood) information on the state of other nodes.
• Some protocols consider fault-tolerant operations on the nodes but other use Entanglement Distillation or Error Corrections schemes on the repeater nodes 5.

## Further Information

All of the approaches below were based on the specific structure of the physical graphs and manipulation of multi-partite entangled states. However, with current day technologies, these solutions are very difficult to realize in practice.

• Distributing entanglement in a simple chain network:
• Distributing entanglement from a percolation theory point of view:
• Distributing Entanglements in a noisy network using the concept of quantum network coding:

The routing approaches below are based on classical techniques and these are arguably more likely to be implemented with the near future quantum technology. In all of these approaches, first, the nodes discover a path from a source to a destination and then distribute the entangled links along the path. The difference between these approaches comes from the path selection algorithms.

Example of optimization metrics of Entanglement Routing Protocols:

Other Works:

## References

Contributed by Lucas Arenstein during the QOSF Mentorship Program
Mentor: Shraddha Singh - Reviewer: Kaushik Chakraborty