  Quantum information measures such as the entropy and the mutual information
find applications in physics, e.g., as correlation measures. Generalizing such
measures based on the R\'enyi entropies is expected to enhance their scope in
applications. We prescribe R\'enyi generalizations for any quantum information
measure which consists of a linear combination of von Neumann entropies with
coefficients chosen from the set {-1,0,1}. As examples, we describe R\'enyi
generalizations of the conditional quantum mutual information, some quantum
multipartite information measures, and the topological entanglement entropy.
Among these, we discuss the various properties of the R\'enyi conditional
quantum mutual information and sketch some potential applications. We
conjecture that the proposed R\'enyi conditional quantum mutual informations
are monotone increasing in the R\'enyi parameter, and we have proofs of this
conjecture for some special cases.
