This protocol implements the functionality of Quantum Electronic Voting. The protocol uses two entangled qudits, one as a blank ballot that travels from voter to voter and the second one for computing the election result. The first quantum scheme in this category was introduced by Vaccaro[1] and later improved by[2,3] .

Quantum protocols for anonymous voting and surveying

Towards quantum-based privacy and voting

We consider $N$ voters who wish to cast their vote secretly.

• The election authority prepares an entangled state, keeps one of the qudits, and passes the other one as the ballot qudit.
• Each voter receives the ballot qudit from the previous voter, casts her vote by applying a unitary and then forwards the qudit to the next voter.
• In the end, the authority obtains the election outcome by measuring the two qudits.

The protocol relies on being able to share a high-dimensional entangled state.

Local parties are assumed to be able to perform local qudit unitaries

Network Stage: Quantum Memory 

Other requirements:

• Quantum channel for qudit communication
• Qudit Measurement Device for the election authority
• Quantum memory to store qudits

• $V_i$: $i^\text{th}$ voter
• $c$: number of possible candidates
• $N$: number of voters
• $v_i$: vote of the $i^\text{th}$ voter
• $T$: election authority
• $m$: number of yes votes

This type of protocol is subject to double voting and privacy attacks when several voters are colluding.

• Double voting: A corrupted voter can apply the “yes” unitary operation many times without being detected.
• Privacy attack: An adversary that corrupts voters $V_{k-1}$ and $V_{k+1}$ can learn how voter $V_{k}$ voted with probability 1.

• Setup phase:
  $T$ prepares the state $|\phi_0\rangle = \dfrac{1}{\sqrt{N}} \sum_{j=0}^{N-1} |j\rangle_V |j\rangle_T$,
  keeps the second qudit and passes the first to voter $V_1$ as the ballot qudit.
• Casting phase:
  For $k = 1, \ldots, N$,
  • $V_k$ receives the ballot qudit and applies the unitary $U^{v_k} = \sum_{j=0}^{N-1} |j+1\rangle \langle j|$,
    where $v_k = 1$ signifies a yes vote and $v_k = 0$ a no vote.
  • Then, $V_k$ forwards the ballot qudit to the next voter $V_{k+1}$ and $V_N$ forwards it to $T$.
• Tallying phase:
  The global state held by $T$ after all voters have voted is:
  $$|\phi_N\rangle = \dfrac{1}{\sqrt{N}} \sum_{j=0}^{N-1} |j+m\rangle_V |j\rangle_T$$

  $T$ measures the two qudits in the computational basis, subtracts the two results, and obtains the outcome $m$.

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