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:<math>\omega \rightarrow (\Phi_x \otimes I)(\omega)</math>
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 Bob's measurement be modelled by a [[POVM]] <math>\{F_y\}_y</math>, with <math>F_y</math> positive semidefinite operators such that <math display="inline">\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 == Experimental ==
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