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Distributed Ballot Based Protocol: Difference between revisions
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==Protocol Description== | ==Protocol Description== | ||
*'''Setup phase''': | |||
# T prepares an N-qudit ballot state <math>|\Phi\rangle= \dfrac{1}{\sqrt{D}}\sum_{j=0}^{D-1}|j\rangle ^{\otimes N}</math>. <p>the states <math> |j\rangle, j = 0,...,D-1,</math> form an orthonormal basis for the D-dimensional Hilbert space, and D > N. The k-th qudit of <math>\Phi</math> corresponds to <math>V_k</math>'s blank ballot.</p> | |||
# T sends to <math>V_k</math> the corresponding blank ballot and two option qudits, one for the "yes" and one for the "no" option:<p><math> yes:|\psi(\theta_y)\rangle=\dfrac{1}{\sqrt{D}}\sum_{j=0}^{D-1}e^{ij\theta_y}|j\rangle</math>, no:<math>|\psi(\theta_n)\rangle=\dfrac{1}{\sqrt{D}}\sum_{j=0}^{D-1}e^{ij\theta_n}|j\rangle</math>.</p> For <math> v\in \{y, n\}</math> we have <math>\theta_v = (2\pi l_v/D) + \delta</math>, where <math>l_v \in \{0,...,D- 1\}</math> and <math>\delta \in [0, 2\pi/D)</math>. Values <math>l_y</math> and <math>\delta</math> are chosen uniformly at random from their domain and <math>l_n</math> is chosen such that <math>N(l_y - l_n \text{ }mod\text{ } D)</math> < D. | |||
*'''Casting phase''': | |||
??? | |||
*'''Tally phase''': | |||
#The global state of the system is: <math> \dfrac{1}{\sqrt{D}}\sum_{j=0}^{D-1}\Pi^{N}_{k=1}\alpha_{j,r_k}|j\rangle^{\otimes 2N}</math> where , <math display="block">\alpha_{j,r_k}= | |||
\begin{cases} | |||
e^{i(D+j-r_k)\theta^{k}_{v}},\text{ }0 \leq j \leq r_k -1,\\ | |||
e^{i(j-r_k)\theta^{k}_{v}}\text{ }r_k \leq j \leq D -1 | |||
\end{cases} | |||
</math> | |||
==Further Information== | ==Further Information== | ||
<div style='text-align: right;'>''*contributed by Sara Sarfaraz''</div> | <div style='text-align: right;'>''*contributed by Sara Sarfaraz''</div> | ||