Strong converse theorems using R\'enyi entropies

Understand

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.