Distributing Graph States Over Arbitrary Quantum Networks: Difference between revisions
Distributing Graph States Over Arbitrary Quantum Networks (edit)
Revision as of 14:37, 11 December 2021
, 11 December 2021Added the properties part. I'm going to send the images by email/slack
(First version of this page. I still need to add the introduction, properties, images and make another good review of everything.) |
(Added the properties part. I'm going to send the images by email/slack) |
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In this protocol a quantum network is represented as a graph | In this protocol a quantum network is represented as a graph | ||
''upload image here'' | '''upload image qn_distributing.svg here''' | ||
<!--[[File:. | <!--[[File:qn_distributing.svg]]--> | ||
The physical distribution of graph states are represented as graph operations ignoring | The physical distribution of graph states are represented as graph operations ignoring | ||
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* <math>|A|</math> number of nodes of A. | * <math>|A|</math> number of nodes of A. | ||
* <math>a_i \in A</math>, <math>i > 0</math> Represents each of the qubits of <math>A</math> that constitutes a Bell pair with a qubit <math>c_i</math> in another node of the network. | * <math>a_i \in A</math>, <math>i > 0</math> Represents each of the qubits of <math>A</math> that constitutes a Bell pair with a qubit <math>c_i</math> in another node of the network. | ||
==Properties== | |||
* The optimality of the protocol depends on the network topology and the wanted graph state to distribute. | |||
* Analysing the consumption of Bell pair between nodes and considering the worst case scenario that is to entangle each qubit with the opposite one over a line network we have the following upper bounds: | |||
{| class="wikitable" | |||
|- | |||
! Distribute | |||
! Cost | |||
! Bound | |||
|- | |||
|rowspan="2"| N-GHZ | |||
| EPR | |||
| <math>N-1</math> | |||
|- | |||
| T | |||
| <math>1</math> | |||
|- | |||
|rowspan="2"| Arbitrary Graph State | |||
| EPR | |||
| <math>\left\lfloor \frac{N}{2} \right\rfloor^2</math> | |||
|- | |||
| T | |||
| <math>\left\lfloor \frac{N}{2} \right\rfloor</math> | |||
|- | |||
|} | |||
==Protocol Description== | ==Protocol Description== | ||
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'''Input''' | '''Input''' | ||
* N-GHZ state: <math>|\text{N-GHZ}\rangle = (|0\rangle^{\otimes N}+|1\rangle^{\otimes N})/\sqrt{2}</math>. | * N-GHZ state: <math>|\text{N-GHZ}\rangle = (|0\rangle^{\otimes N}+|1\rangle^{\otimes N})/\sqrt{2}</math>. | ||
* That is locally equivalent to: <math>(|0\rangle|+\rangle^{\otimes N-1}+|1\rangle|-\rangle^{\otimes N-1})/\sqrt{2}</math> that is called a star graph ''' | * That is locally equivalent to: <math>(|0\rangle|+\rangle^{\otimes N-1}+|1\rangle|-\rangle^{\otimes N-1})/\sqrt{2}</math> that is called a star graph '''upload image star_graph_distributing.svg here''' | ||
<!-- | <!--[[File:star_graph_distributing.svg]]--> | ||
* Arbitrary set <math>W</math> of the network nodes. | * Arbitrary set <math>W</math> of the network nodes. | ||