Quantum states have the property of superposition, meaning that the same quantum bit can be in multiple states simultaneously. This superposition characteristic will increase the uncertainty of the distribution network system, making it difficult to accurately control the state variations in distribution network system, increasing energy consumption, and reducing the overall performance of the distribution network system. Therefore, a method for multi-objective operation of distribution network systems during the day under quantum communication optimization is proposed. The introduction of quantum communication enables it to cope with high uncertainty in the scheduling process, ensure secure data transmission, and improve scheduling efficiency. By utilizing the high security, large capacity transmission, and strong anti-interference ability of quantum communication, we can solve the limitations of traditional communication methods in distribution network scheduling. On the basis of calculating power loss cost, collaborative control investment cost, and flexible load cost, this method constructs a multi-objective collaborative optimization model. At the same time, considering the characteristics of quantum communication, constraints including power balance, distribution network operation balance, flexible load transfer balance, and load fluctuation are established to better adapt the model to the quantum communication environment. In order to solve this multi-objective collaborative optimization model, the imperial competition algorithm is combined with genetic algorithm, and the concept of quantum state probability is introduced. By improving the population evolution and gene combination process of the imperial competition algorithm through cross operation of genetic algorithm, we can avoid getting stuck in local optima and achieve optimized collaborative control of quantum communication distribution network system. In simulation testing, the proposed method significantly reduced the power loss of the distribution network at a time scale of 12 hours per day, making it below 50 kW. In contrast, the power loss of existing research methods is higher than 60 kW. Meanwhile, the economic cost of the proposed method for the distribution network has also been reduced by CNY 500000 compared to other methods. This result indicates that the proposed quantum communication distribution network optimization collaborative control method has a significant effect on improving system economy and stability, which can ensure the safe and stable operation of the quantum communication distribution network system within the intra-day time scale.