  We use a R\'enyi entropy method to prove strong converse theorems for certain
information-theoretic tasks which involve local operations and quantum or
classical communication between two parties. These include state
redistribution, coherent state merging, quantum state splitting, measurement
compression with quantum side information, randomness extraction against
quantum side information, and data compression with quantum side information.
The method we employ in proving these results extends ideas developed by Sharma
[arXiv:1404.5940], which he used to give a new proof of the strong converse
theorem for state merging. For state redistribution, we prove the strong
converse property for the boundary of the entire achievable rate region in the
$(e,q)$-plane, where $e$ and $q$ denote the entanglement cost and quantum
communication cost, respectively. In the case of measurement compression with
quantum side information, we prove a strong converse theorem for the classical
communication cost, which is a new result extending the previously known weak
converse. For the remaining tasks, we provide new proofs for strong converse
theorems previously established using smooth entropies. For each task, we
obtain the strong converse theorem from explicit bounds on the figure of merit
of the task in terms of a R\'enyi generalization of the optimal rate. Hence, we
identify candidates for the strong converse exponents for each task discussed
in this paper. To prove our results, we establish various new entropic
inequalities, which might be of independent interest. These involve conditional
entropies and mutual information derived from the sandwiched R\'enyi
divergence. In particular, we obtain novel bounds relating these quantities, as
well as the R\'enyi conditional mutual information, to the fidelity of two
quantum states.
