where ''I'' denotes the identity map on subsystem 2. Alice then sends her subsystem to Bob, who performs a measurement on the combined system to recover the message. Let the ''effects'' of Bob's measurement be ''Fmodelled by a [[POVM]] <submath>y\{F_y\}_y</submath>, with <math>F_y</math> positive semidefinite operators such that <math>\sum_y F_y=I</math>''. The probability that Bob's measuring apparatus registers the message <math>y</math> is thus<math display="block">p(y|x)=\langle F_y, (\Phi_x \otimes I)(\omega)\rangle\equiv \operatorname{Tr}[ F_y(\Phi_x \otimes I)(\omega)].</math>Therefore, to achieve the desired transmission, we require that<math display="block">p(y|x)=\operatorname{Tr}[F_y (\Phi_x \otimes I)(\omega)] = \delta_{xy}</math>where ''yδ<sub>xy</sub>'' is the [[Kronecker delta]].
