Editing Travelling Ballot Based Protocol (section)

==Protocol Description==
*Setup phase:
T prepares the state <math>|\phi_0\rangle =\dfrac{1}{\sqrt{N}}\sum_{j=0}^{N-1}|j\rangle_V |j\rangle_T</math>, keeps the second qudit and passes the first to voter <math> V_1</math> as the ballot qudit.

* Casting phase:
For k = 1, ... ,N, <math>V_k </math>receives the ballot qudit and applies the unitary <math>U^{v_{k}}=\sum_{j=0}^{N-1}|j+1\rangle \langle j|</math>, where <math>v_k = 1</math> signifies a yes vote and <math>v_k = 0</math> a no vote. 

Then, <math> V_k</math> forwards the ballot qudit to the next voter <math>V_{k+1}</math> and <math> V_N</math> to T.


* Tallying phase:
The global state held by T after all voters have voted is:
<math>|\phi_N\rangle =\dfrac{1}{\sqrt{N}}\sum_{j=0}^{N-1}|j+m\rangle_V|j\rangle_T</math>
T measures the two qudits in the computational basis, subtracts the two results, and obtains the outcome m.