We introduce a quantum voting protocol that uses superposition and entanglement to enable secure, anonymous voting in both centralized and distributed settings. Votes are encoded via phase-flip operations on entangled candidate states, controlled by voter identity registers. Tallying is performed directly by measuring the candidate register, eliminating the need for iterative classical counting. The protocol is described for a centralized single-machine model and extended to a distributed quantum channel model with entanglement-based verification for enhanced security. Its efficiency relies on basic quantum gates (Hadamard and controlled-Z) and the ability to extract vote counts from quantum measurements. Practical validation is provided through analytical examples (4 voters with 2 candidates and 8 voters with 3 candidates) as well as numerical experiments that simulate ideal conditions, depolarizing noise, dishonest voter attacks, and sampling convergence. The results confirm exact probability preservation, robustness against errors, and statistical behavior consistent with theoretical bounds. The protocol ensures voter anonymity via superposition, prevents double-voting through entanglement mechanisms, and offers favorable complexity for large-scale elections.

翻译：我们提出一种量子投票协议，该协议利用叠加态与纠缠态在集中式和分布式场景中实现安全匿名投票。选票通过选民身份寄存器控制的纠缠候选态相位翻转操作进行编码，计票过程直接通过测量候选寄存器完成，无需迭代式经典计数。该协议在集中式单机模型上描述后，进一步扩展至基于纠缠验证的分布式量子信道模型以增强安全性。其效率依赖于基础量子门（Hadamard门和受控Z门）以及从量子测量中提取票数的能力。通过分析示例（2候选4选民与3候选8选民）及模拟理想条件、退极化噪声、不诚实选民攻击与采样收敛性的数值实验，提供了实际验证。结果证实了精确概率保持性、误差鲁棒性以及与理论边界一致的统计行为。该协议通过叠加态保障选民匿名性，通过纠缠机制防止重复投票，并在大规模选举中展现出良好的复杂度。