On conditional Sibson's $\alpha$ -Mutual Information

Amedeo Roberto Esposito, Diyuan Wu, Michael Gastpar

Abstract: In this work, we analyse how to define a conditional version of Sibson's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> -Mutual Information. Several such definitions can be advanced and they all lead to different information measures with different (but similar) operational meanings. We will analyse in detail one such definition, compute a closed-form expression for it and endorse it with an operational meaning while also considering some applications. The alternative definitions will also be mentioned and compared.