Editing Practical Quantum Electronic Voting (section)

===Protocol 3 : Verification===
''Input'': A quantum state distributed and shared by <math>N</math> parties, security parameter <math>S</math> for '''RandomAgent'''.

''Output'': If the state is a GHZ state <math> \rightarrow </math> YES.

''Resources'': Classical communication, random numbers, quantum state source, quantum channels.

# Everyone executes '''RandomAgent''' to choose uniformly at random one of the voters to be the verifier.
# The verifier generates random angles <math>\theta_j \in [0, \pi)</math> for all agents including themselves, such that the sum is a multiple of <math>\pi</math>. The angles are then sent out to all the agents.
# Agent <math>j</math> measures in the basis <math>[|+_\theta\rangle,|-_\theta\rangle] = [\frac{1}{\sqrt{2}}(|0\rangle + e^{i\theta_j}|1\rangle), \frac{1}{\sqrt{2}}(|0\rangle - e^{i\theta_j}|1\rangle)]</math> and publicly announces the result <math>Y_j = \{0,1\}</math>
# The state passes the verification test when the following condition is satisfied: if the sum of the randomly chosen angles is an even multiple of <math>\pi</math>, there must be an even number of 1 outcomes for <math>Y_j</math> , and if the sum is an odd multiple of <math>\pi</math>, there must be an odd number of 1 outcomes for <math>Y_j : \bigoplus_j Y_j = \frac{1}{\pi}\sum_i\theta_i </math> (mod 2)