Many problems of error analysis in quantum information processing can be formulated as deviation inequalities of random matrices. In this talk, I will talk about how complex interpolations of various Lp spaces can be an effective tool in establishing error estimates in information tasks such as quantum soft covering, privacy amplification, convex splitting and quantum decoupling.  This talk is based on joint works with Hao-Chung Cheng, Yu-Chen Shen, Frédéric Dupuis and Mario Berta.