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Dual Basis Measurement Based Protocol: Difference between revisions
→Protocol Description
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# <p>One of the voters, not necessarily trusted, prepares <math> N+N2^{\delta_0}</math> states of the form <math>|D_1\rangle=\dfrac{1}{\sqrt{m^{N-1}}}\sum_{\sum_{k=1}^{N}i_k=0\text{ } mod \text{ }c}|i_1\rangle|i_2\rangle...|i_N\rangle </math> and <math> 1 + N2^{\delta_0}</math> states of the form <math> |D_2\rangle=\dfrac{1}{\sqrt{N!}}\sum_{(i_1,i_2,...,i_N)\in P_N}|i_1\rangle|i_2\rangle...|i_N\rangle </math>. </p> Each voter <math>V_k</math> receives kth particle from each of the states. | # <p>One of the voters, not necessarily trusted, prepares <math> N+N2^{\delta_0}</math> states of the form <math>|D_1\rangle=\dfrac{1}{\sqrt{m^{N-1}}}\sum_{\sum_{k=1}^{N}i_k=0\text{ } mod \text{ }c}|i_1\rangle|i_2\rangle...|i_N\rangle </math> and <math> 1 + N2^{\delta_0}</math> states of the form <math> |D_2\rangle=\dfrac{1}{\sqrt{N!}}\sum_{(i_1,i_2,...,i_N)\in P_N}|i_1\rangle|i_2\rangle...|i_N\rangle </math>. </p> Each voter <math>V_k</math> receives kth particle from each of the states. | ||
# Voter <math>V_k</math> chooses at random <math>2^{\delta_0}</math> of the <math>|D_1\rangle</math> states The other voters measure half of their particles in the computational and half in the Fourier basis. Whenever the chosen basis is computational, the measurement results need to add up to 0, while when the basis is the Fourier, the measurement results are all the same. All voters simultaneously broadcast their results and if one of them notices a discrepancy, the protocol aborts.<p> The states <math>|D_2\rangle</math> are similarly checked.</p> | # Voter <math>V_k</math> chooses at random <math>2^{\delta_0}</math> of the <math>|D_1\rangle</math> states The other voters measure half of their particles in the computational and half in the Fourier basis. Whenever the chosen basis is computational, the measurement results need to add up to 0, while when the basis is the Fourier, the measurement results are all the same. All voters simultaneously broadcast their results and if one of them notices a discrepancy, the protocol aborts.<p> The states <math>|D_2\rangle</math> are similarly checked.</p> | ||
#<p> All voters measure their qudits in the computational basis.</p> Then each <math>V_k</math> holds a blank ballot of dimension N with the measurement outcomes corresponding to parts of <math>|D_1\rangle </math> states <math>B_k = [\xi_k^{1}...\xi_k^{sk_k}...\xi_k^{N}]^{T}</math> and a unique index, <math>sk_k \in \{1,...,N\}</math> from the measurement outcome of the | #<p> All voters measure their qudits in the computational basis.</p> Then each <math>V_k</math> holds a blank ballot of dimension N with the measurement outcomes corresponding to parts of <math>|D_1\rangle </math> states <math>B_k = [\xi_k^{1}...\xi_k^{sk_k}...\xi_k^{N}]^{T}</math> and a unique index, <math>sk_k \in \{1,...,N\}</math> from the measurement outcome of the qudit that belongs to <math>|D_2\rangle</math>. | ||
qudit that belongs to <math>|D_2\rangle</math>. | |||
*'''Casting phase''': | |||
# <math>V_k</math> applies <math>\xi^{sk_k}_k\rightarrow \xi^{sk_k}_k+v_k</math>. | |||
# All voters simultaneously broadcast their columns resulting in a public <math>N \times N table.</math> | |||
*'''Tally phase''': | |||
# Each <math>V_k</math> checks that the corresponding row of the matrix adds up to their vote. If this fails, the protocol aborts. | |||
# final outcome of the election is the sum of the elements of each row of the public <math>N \times N</math> table | |||
==Further Information== | ==Further Information== | ||