Partition tree X∈{0,1}” Index(x,i)=xi ie[n] Alice Px Bob ·p=∑xPxPx 000 001 ·pb=2∑xxi=o Px"Px Po 010 P01 011 ·Pb1b2= 100 p10 4∑xx1=b1,x2=b2PxPx 101 P11< 110 111Partition tree • ρ = ∑x px ∙ρx • ρb = 2 ∑x:x1=b px ∙ρx • ρb1b2 = 4 ∑x:x1=b1,x2=b2 px ∙ρx 000 001 010 011 100 101 110 111 ρ00 ρ01 ρ10 ρ11 ρ0 ρ1 ρ Alice Bob x{0,1}n i[n] Index(x,i) = xi ρx