In personalized federated learning (PFL), multiple clients train customized models to fulfill their personal objectives, which, however, are prone to overfitting to local data due to the heterogeneity and scarcity of local data. To address this, we propose from the information-theoretic perspective a personalized federated learning framework based on the common representation learned across clients, named FedCR. Specifically, we introduce to the local client update a regularizer that aims at minimizing the discrepancy between local and global conditional mutual information (CMI), such that clients are encouraged to learn and exploit the common representation. Upon this, each client learns individually a customized predictor (head), while the extractor (body) remains to be aggregated by the server. Our CMI regularizer leads to a theoretically sound alignment between the local and global stochastic feature distributions in terms of their Kullback-Leibler (KL) divergence. More importantly, by modeling the global joint feature distribution as a product of multiple local feature distributions, clients can efficiently extract diverse information from the global data but without need of the raw data from other clients. We further show that noise injection via feature alignment and ensemble of local predictors in FedCR would help enhance its generalization capability. Experiments on benchmark datasets demonstrate a consistent performance gain and better generalization behavior of FedCR.