Editing Distributed Ballot Based Protocol
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 28: | Line 28: | ||
==Protocol Description== | ==Protocol Description== | ||
*'''Setup phase''': | *'''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> | # 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,for the "yes" and "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 | # 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''': | *'''Casting phase''': | ||
??? | |||
*'''Tally 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}= | #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}= | ||
Line 38: | Line 38: | ||
e^{i(j-r_k)\theta^{k}_{v}}\text{ }r_k \leq j \leq D -1 | e^{i(j-r_k)\theta^{k}_{v}}\text{ }r_k \leq j \leq D -1 | ||
\end{cases} | \end{cases} | ||
</math> | </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> |