Routing Entanglement in the Quantum Internet: Difference between revisions
Routing Entanglement in the Quantum Internet (edit)
Revision as of 17:34, 11 December 2021
, 11 December 2021Added the introduction, a small edit in the protocol description, the Properties and Further Information section.
(First version of the page made by Lucas. I still need to add some parts and make another good review of everything.) |
(Added the introduction, a small edit in the protocol description, the Properties and Further Information section.) |
||
| Line 4: | Line 4: | ||
<!-- Intro: brief description of the protocol --> | <!-- Intro: brief description of the protocol --> | ||
<!-- to do --> | <!-- to do --> | ||
This [https://www.nature.com/articles/s41534-019-0139-x example protocol (1)] implements the task of [[Entanglement Routing]] considering different scenarios. All of the protocols presented are applicable to quantum networks with arbitrary topology but their analysis is only concerned with the 2D grid network. They develop protocols for multipath routing of a single entanglement flow with global or local state information of the other quantum repeater nodes and a protocol for multipath routing of simultaneous entanglement flows with repeaters with local state information. | |||
'''Tags:''' [[:Category: Multi Party Protocols|Multi Party]], [[:Category: Specific Task|Specific Task]]. | |||
<!-- I'm not sure if it is a Building Block or not [[:Category:Building Blocks|Building Block]] --> | |||
<!--Tags: related pages or category --> | <!--Tags: related pages or category --> | ||
<!-- to do --> | <!-- to do --> | ||
| Line 28: | Line 32: | ||
The high-level objective is: Considering the assumptions of quantum and classical operations at each of the repeater nodes of the underlying network, what operations should be performed at the repeater to achieve maximum entanglement-generation rate for one sender and receiver or achieve maximum rate region for multiple flows of entanglement. | The high-level objective is: Considering the assumptions of quantum and classical operations at each of the repeater nodes of the underlying network, what operations should be performed at the repeater to achieve maximum entanglement-generation rate for one sender and receiver or achieve maximum rate region for multiple flows of entanglement. | ||
==Notation== | ==Notation== | ||
| Line 50: | Line 52: | ||
<!-- Add this part if the protocol is already in the graph --> | <!-- Add this part if the protocol is already in the graph --> | ||
<!--{{graph}} --> | <!--{{graph}} --> | ||
==Protocol Description== | ==Protocol Description== | ||
<!-- Mathematical step-wise protocol algorithm helpful to write a subroutine. --> | <!-- Mathematical step-wise protocol algorithm helpful to write a subroutine. --> | ||
| Line 63: | Line 60: | ||
** Each of the <math>S(e)</math> pairs of memories across and edge <math>e</math> attempts to establish an EPR pair. | ** Each of the <math>S(e)</math> pairs of memories across and edge <math>e</math> attempts to establish an EPR pair. | ||
*:- An entanglement attempt across any one of the <math>S(e)</math> parallel links across edge <math>e</math> succeeds with probability <math>p_0(e) \sim \eta(e)</math>, where <math>\eta(e) \sim e^{-\alpha L_e}</math> is the transmissivity of a lossy optical channel of length <math>L(e)</math>. | *:- An entanglement attempt across any one of the <math>S(e)</math> parallel links across edge <math>e</math> succeeds with probability <math>p_0(e) \sim \eta(e)</math>, where <math>\eta(e) \sim e^{-\alpha L_e}</math> is the transmissivity of a lossy optical channel of length <math>L(e)</math>. | ||
*:- The probability that one or more ebits are established across an edge <math>e</math> is <math>p(e)=1-(1-p_0)^{S(e)}</math>. | |||
*:- Assuming <math>S(e)=S,</math> give us <math>p(e)=p,</math> <math>\forall e \in E</math>. | |||
** Using two-way classical communication over edge <math>e(u, v)</math>, neighboring repeater nodes <math>u, v</math> learn which of the S(e) parallel links (if any) succeeded in the external phase, in a given time slot. | ** Using two-way classical communication over edge <math>e(u, v)</math>, neighboring repeater nodes <math>u, v</math> learn which of the S(e) parallel links (if any) succeeded in the external phase, in a given time slot. | ||
* '''Internal Phase:''' | * '''Internal Phase:''' | ||
** BSMs are attempted locally at each repeater node between pairs of qubit memories based on the success and failure of the neighboring links in the external phase. | ** BSMs are attempted locally at each repeater node between pairs of qubit memories based on the success and failure of the neighboring links in the external phase. | ||
| Line 124: | Line 121: | ||
** Considering the square-grid topology the two spatial regions are divided by two crossing lines with an angle <math>\theta</math> between them (forming a hourglass shape). | ** Considering the square-grid topology the two spatial regions are divided by two crossing lines with an angle <math>\theta</math> between them (forming a hourglass shape). | ||
** For each one of this regions we apply the Protocol for Entanglement Routing with Local Link-state Information. | ** For each one of this regions we apply the Protocol for Entanglement Routing with Local Link-state Information. | ||
==Properties== | |||
<!-- important information on the protocol: parameters (threshold values), security claim, success probability... --> | |||
<!-- to do --> | |||
* The goal of the optimal repeater strategy is to achieve: | |||
** Maximum entanglement generation rate for a single sender and receiver (<math>K=1</math>). | |||
*:- Above a (percolation) threshold determined by <math>p</math> and <math>q</math> the entanglement generation rate will depend only linearly on the transmissivity <math>\eta</math> of a single link in the network. | |||
* Maximum rate regions simultaneously achievable by the entanglement flows (<math>K \geq 2</math>). | |||
*:- Above a (percolation) threshold determined by <math>p</math> and <math>q</math> this protocol significantly exceeds the ones that each repeater node makes BSM decisions by simply time-sharing between catering to the individual flows. | |||
==Further Information== | ==Further Information== | ||
<!-- theoretical and experimental papers including requirements, security proof (important), which protocol does it implement, benchmark values... --> | <!-- theoretical and experimental papers including requirements, security proof (important), which protocol does it implement, benchmark values... --> | ||
<!-- to do --> | <!-- to do --> | ||
* [https://arxiv.org/abs/1601.00966 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. | |||
* [https://arxiv.org/abs/1606.00135 Azuma and Kato (2016)] looked at an "aggregated" protocol in which the repeater protocols run in parallel. | |||
* [https://arxiv.org/abs/1610.05238 Schoute et al. (2016)] developed routing protocols on specific network topologies and found scaling laws as functions on the number of qubits in the memories at nodes, and the time and space consumed by the routing algorithms, under lossless and noiseless assumptions. | |||
* [https://arxiv.org/abs/quant-ph/0612167 Acín et al. (2006)] have considered the problem of entanglement percolation where neighboring nodes share a perfect lossless pure state. | |||
There is an extensive literature of quantum networks analyzing repeaters in a linear chain for example: | |||
[https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.81.5932 Briegel et al. (1998)], [https://arxiv.org/abs/0809.3629 Jiand et al. (2008)] and [https://www.nature.com/articles/srep20463 Muralidharan et al. (2016)]. | |||
==References== | ==References== | ||
<!-- to do --> | <!-- to do --> | ||
# [https://www.nature.com/articles/s41534-019-0139-x Pant et al. (2019)] | |||
<div style='text-align: right;'>''*contributed by Lucas Arenstein''</div> | <div style='text-align: right;'>''*contributed by Lucas Arenstein''</div> | ||