Submartingale Property of E_0 Under The Polarization Transformations

We prove that the relation $E_0(\rho, W^{-}) + E_0(\rho, W^{+}) \geq 2 E_0(\rho, W)$holdsforanybinaryinputdiscretememorylesschannel$W$,and$\rho \geq 0$.