Editing Entanglement Routing

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==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.

'''Tags:'''  [[:Category: Multi Party Protocols|Multi Party]], [[:Category: Specific Task|Specific Task]].
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==Use Case==
*No classical analogue.

==Protocols==
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* Almost all of the protocols within this functionality are in the [[:Category: Quantum Memory Network Stage|Quantum Memory Network Stage]].
Entanglement routing protocol:
* [[Routing Entanglement in the Quantum Internet]]
* [[Distributed Routing in a Quantum Internet]]
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Related protocol:
* [[Distributing Graph States Over Arbitrary Quantum Networks]]

==Properties==
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* 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 [https://en.wikipedia.org/wiki/Entanglement_distillation Entanglement Distillation] or Error Corrections schemes on the repeater nodes [https://www.nature.com/articles/s41534-021-00438-7 5].

==Further Information==
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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:
** For a review: [https://ieeexplore.ieee.org/document/7010905 Munro et al. (2015)]
** [https://arxiv.org/abs/0705.4128 Meter et al. (2009)]
** [https://arxiv.org/abs/0808.2972 Goebel et al. (2008)]
** [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.5932 Briegel et al. (1998)]

* Distributing entanglement from a percolation theory point of view:
** [https://arxiv.org/abs/1209.5303 Perseguers et al. (2013)]
** [https://www.nature.com/articles/nphys549 Acín et al. (2007)]
** [https://arxiv.org/abs/0906.1622 Broadfoot et al. (2009)]

* Distributing Entanglements in a noisy network using the concept of quantum network coding:
<!-- ** [https://arxiv.org/abs/0807.0208 Perseguers et al. (2008)] -->
** [https://arxiv.org/abs/0910.4074 Fowler et al. (2010)]
** [https://arxiv.org/abs/0910.1459 Perseguers (2010)]
** [https://arxiv.org/abs/1202.4077 Cavalcanti and Kwek (2012)]
** [https://arxiv.org/abs/1202.1016 Mazurek et al. (2014)]

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.
* [https://ieeexplore.ieee.org/document/8068178 Caleffi (2017)]
* [https://arxiv.org/abs/1801.02020 Gyongyosi and Imre (2018)]
* [https://arxiv.org/abs/1206.5655 Meter et al. (2013)]
* [https://arxiv.org/abs/1610.05238 Schoute et al. (2016)]

Example of optimization metrics of Entanglement Routing Protocols:
* In [[Routing Entanglement in the Quantum Internet]] their goal is to maximize the rate regions simultaneously achievable by the entanglement flows
* In [[Distributed Routing in a Quantum Internet]] their objective is to minimize the latency of the network to serve a request to create entanglement between two distant nodes in the network.
* In [https://ieeexplore.ieee.org/document/9210823 Entanglement Distribution in a Quantum Network: A Multicommodity Flow-Based Approach - Chakraborty et al. (2020)] they consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs.

Other Works:
* In [https://arxiv.org/abs/1601.00966 Capacities of repeater-assisted quantum communications - Pirandola (2016)] analyzed entanglement-generation capacities of repeater networks assuming ideal repeater nodes and argued that for a single ﬂow the maximum entanglement-generation rate <math>R_1</math> reduces to the classical max-ﬂow min-cut problem.
* In [https://arxiv.org/abs/1510.08863 Fundamental Limits of Repeaterless Quantum Communications - Pirandola et al. (2015)] provides precise and general benchmarks for quantum repeaters. 

==References==
# [https://arxiv.org/abs/1610.05238 Schoute et al. Shortcuts to Quantum Network Routing (2016)]
# [https://arxiv.org/abs/1907.11630 Chakraborty et al. (2019)] - [[Distributed Routing in a Quantum Internet]]
# [https://www.nature.com/articles/s41534-019-0139-x Pant et al. Routing entanglement in the quantum internet (2019)] - [[Routing Entanglement in the Quantum Internet]]
# [https://dl.acm.org/doi/10.1145/3387514.3405853 Shi and Qian, Concurrent Entanglement Routing for Quantum Networks: Model and Designs (2020)]
# [https://www.nature.com/articles/s41534-021-00438-7 Rozpędek et al. Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes (2021)]

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<div style='text-align: right;'>''Contributed by Lucas Arenstein during the QOSF Mentorship Program''</div>
<div style='text-align: right;'>''Mentor: Shraddha Singh - Reviewer: Kaushik Chakraborty </div>