Continuity inequalities for sandwiched Rényi and Tsallis conditional entropies with application to the channel entropy continuity

Anna Vershynina

For the sandwiched Rényi entropy the conditional entropy can be defined two ways: ${\tilde{H}}_{\alpha }^{\downarrow }(A|B{)}_{\rho },{\tilde{H}}_{\alpha }^{\uparrow }(A|B{)}_{\rho }$. In the limiting case, $\alpha =1$,…