Editing Verifiable Quantum Anonymous Transmission (section)

==Outline==
This verified GHZ-based quantum anonymous transmission protocol is based on the work of [[Verifiable Quantum Anonymous Transmission#References|[1]]], which uses the following subroutines from [[Verifiable Quantum Anonymous Transmission#References|[2]]], [[Verifiable Quantum Anonymous Transmission#References|[3]]], [[Verifiable Quantum Anonymous Transmission#References|[4]]], [[Verifiable Quantum Anonymous Transmission#References|[5]]] :
* <span style="font-variant:small-caps">Parity</span> [[Verifiable Quantum Anonymous Transmission#References|[3]]]: privately computes the parity of an input string.
* <span style="font-variant:small-caps">LogicalOR</span> [[Verifiable Quantum Anonymous Transmission#References|[3]]]: privately computes the logical OR of an input string, using a modified version of <span style="font-variant:small-caps">Parity</span>.
* <span style="font-variant:small-caps">Notification</span> [[Verifiable Quantum Anonymous Transmission#References|[3]]]: allows one player to anonymously notify another player, using <span style="font-variant:small-caps">LogicalOR</span>.
* <span style="font-variant:small-caps">RandomBit</span> [[Verifiable Quantum Anonymous Transmission#References|[1]]]: allows one player to anonymously choose a bit according to a probability distribution, using <span style="font-variant:small-caps">LogicalOR</span>.
* <span style="font-variant:small-caps">[https://wiki.veriqloud.fr/index.php?title=Multipartite_Entanglement_Verification Verification]</span> [[Verifiable Quantum Anonymous Transmission#References|[4,5]]]: allows one player (the Verifier) to run a test to check if the shared state is the GHZ state. The Verifier instructs each player to measure their qubit in a particular basis and checks the parity of the measurement outcomes. 
* <span style="font-variant:small-caps">Anonymous Entanglement</span> [[Verifiable Quantum Anonymous Transmission#References|[2]]]: <math>n-2</math> nodes (all except for <math>\mathcal{S}</math> and <math>\mathcal{R}</math>) measure in the <math>X</math> basis and broadcast their measurement outcome. <math>\mathcal{S}</math> and <math>\mathcal{R}</math> broadcast random dummy bits. The parity of measurement outcomes allows the establishment of an entangled link between <math>\mathcal{S}</math> and <math>\mathcal{R}</math> which is called anonymous entanglement.

The protocol for quantum anonymous transmission consists of the following steps:
# ''Receiver notification'': The Sender <math>\mathcal{S}</math> notifies the Receiver <math>R</math> by running <span style="font-variant:small-caps">Notification</span>.
# ''State distribution'': A source, who may be untrusted, distributes a state claiming to be the GHZ state.
# ''Verification or anonymous transmission'': <math>\mathcal{S}</math> anonymously chooses whether to verify the state or use it for anonymous transmission, using <span style="font-variant:small-caps">RandomBit</span>. 

If verification is chosen, a player is chosen to run <span style="font-variant:small-caps">Verification</span>, using <math>\log_2 n</math> repetitions of  <span style="font-variant:small-caps">RandomBit</span>. 
If the test passes, the protocol goes back to the ''State distribution'' stage and runs again. If the test fails, the players abort. 

If anonymous transmission is chosen, the players run <span style="font-variant:small-caps">Anonymous Entanglement</span>, establishing an anonymous entanglement link between <math>\mathcal{S}</math> and <math>\mathcal{R}</math>.
<math>\mathcal{S}</math> then teleports the message state <math>|\psi\rangle</math> to <math>\mathcal{R}</math> using the established anonymous entanglement. The classical message <math>m</math> associated with teleportation is also sent anonymously.