Quorum sensing is the regulation of gene expression in response to changes in cell density. To measure their cell density, bacterial populations produce and detect diffusible molecules called autoinducers. Individual bacteria internally represent the external concentration of autoinducers via the level of monitor proteins. In turn, these monitor proteins typically regulate both their own production and the production of autoinducers, thereby establishing internal and external feedbacks. Here, we ask whether feedbacks can increase the information available to cells about their local density. We quantify available information as the mutual information between the abundance of a monitor protein and the local cell density for biologically relevant models of quorum sensing. Using variational methods, we demonstrate that feedbacks can increase information transmission, allowing bacteria to resolve up to two additional ranges of cell density when compared with bistable quorum-sensing systems. Our analysis is relevant to multi-agent systems that track an external driver implicitly via an endogenously generated signal.