Dual Basis Measurement Based Protocol

This example protocol implements the task of |Quantum E-voting. The protocol uses an entangled state with a special property as a blank ballot and is self-tallying i.e. The voters, without the presence of any trusted authority or tallier, need to verify that they share specific quantum states.

Assumptions

• all classical communication in the protocol takes place using pairwise authenticated channels.

Outline

We consider N voters who wish to cast their vote secretly. One of the voters prepares some states in two forms and each voter receives a specific particle of each state. After voters verify that they received correct states by cut and choose technique, they perform certain measurements on their qudits and cast their vote based on the measurement outcome.

In the end, all voters simultaneously broadcast their votes in encoded form and everyone can compute the election result by a simple summation.

Notations

• $V_{i}:i^{th}$ voter
• c: number of possible candidates
• m: dimension of qudits
• $\delta _{0}$: security parameter
• N: number of voters
• $v_{i}$: vote of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle i^{th}} voter
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_{N}} : set of all possible permutations with N elements
• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_{k}: k^{th}} voter’s blank ballot