This paper proposes a quantum image encryption algorithm based on a four-dimensional chaotic system. The algorithm uses the Generalized Quantum Image Representation (GQIR) method to encode classical images into quantum information. A four-dimensional chaotic system is then used to generate random keys for initial pixel encryption, followed by the Arnold transformation to randomize pixel positions. During decryption, the inverse process is applied to restore the original image. The algorithm demonstrates high information entropy, with encrypted images achieving entropy values above 7.999, indicating strong encryption. The pixel correlation after encryption is weak, showing that the chaotic system's control parameters effectively reduce pixel correlation. The key space of the encryption algorithm is extremely large, reaching $10^{140}$, which provides strong resistance to statistical attacks. The algorithm combines the Arnold transformation with a four-dimensional chaotic system to enhance encryption security. It uses the characteristics of the Arnold transformation, ergodicity, and randomness of the four-dimensional chaotic system to achieve high encryption and usability. The algorithm is resistant to various attacks, including statistical and brute force attacks, and produces scrambled images with enhanced security and usability. The encryption process involves quantum operations, including the Arnold transformation and quantum adder, to achieve secure image encryption. The decryption process reverses these operations to retrieve the original image. The algorithm is tested on grayscale images, showing high information entropy, uniform histogram distribution, and low pixel correlation, indicating strong encryption performance. The algorithm is robust against various attacks, including differential attacks and chosen-plaintext attacks. The key sensitivity analysis shows that even minor key deviations prevent the correct decryption of the image. The algorithm's key space is sufficiently large to resist destructive attacks, and the encryption process is performed using reversible quantum logic gates to enhance the quality of the decrypted image. The study concludes that the proposed quantum image encryption algorithm based on a four-dimensional chaotic system is effective and secure, providing a reliable solution for quantum image encryption. The algorithm addresses the shortcomings of traditional encryption methods, such as periodicity and small key space, and offers a robust and efficient encryption scheme.This paper proposes a quantum image encryption algorithm based on a four-dimensional chaotic system. The algorithm uses the Generalized Quantum Image Representation (GQIR) method to encode classical images into quantum information. A four-dimensional chaotic system is then used to generate random keys for initial pixel encryption, followed by the Arnold transformation to randomize pixel positions. During decryption, the inverse process is applied to restore the original image. The algorithm demonstrates high information entropy, with encrypted images achieving entropy values above 7.999, indicating strong encryption. The pixel correlation after encryption is weak, showing that the chaotic system's control parameters effectively reduce pixel correlation. The key space of the encryption algorithm is extremely large, reaching $10^{140}$, which provides strong resistance to statistical attacks. The algorithm combines the Arnold transformation with a four-dimensional chaotic system to enhance encryption security. It uses the characteristics of the Arnold transformation, ergodicity, and randomness of the four-dimensional chaotic system to achieve high encryption and usability. The algorithm is resistant to various attacks, including statistical and brute force attacks, and produces scrambled images with enhanced security and usability. The encryption process involves quantum operations, including the Arnold transformation and quantum adder, to achieve secure image encryption. The decryption process reverses these operations to retrieve the original image. The algorithm is tested on grayscale images, showing high information entropy, uniform histogram distribution, and low pixel correlation, indicating strong encryption performance. The algorithm is robust against various attacks, including differential attacks and chosen-plaintext attacks. The key sensitivity analysis shows that even minor key deviations prevent the correct decryption of the image. The algorithm's key space is sufficiently large to resist destructive attacks, and the encryption process is performed using reversible quantum logic gates to enhance the quality of the decrypted image. The study concludes that the proposed quantum image encryption algorithm based on a four-dimensional chaotic system is effective and secure, providing a reliable solution for quantum image encryption. The algorithm addresses the shortcomings of traditional encryption methods, such as periodicity and small key space, and offers a robust and efficient encryption scheme.