This paper presents an anomaly detection model that combines the strong statistical foundation of density-estimation-based anomaly detection methods with the representation-learning ability of deep-learning models. The method combines an autoencoder, that learns a low-dimensional representation of the data, with a density-estimation model based on density matrices in an end-to-end architecture that can be trained using gradient-based optimization techniques. A systematic experimental evaluation was performed on different benchmark datasets. The experimental results show that the method is able to outperform other state-of-the-art methods.