Superdense coding: Difference between revisions

Revision as of 01:54, 30 September 2011

Revision as of 10:17, 7 May 2012

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on subsystem 1. On the combined system, this is effected by

:<math>\omega \rightarrow (\Phi_x \otimes IdI)(\omega)</math>

where ''IdI'' 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 ''F_y''. The probability that Bob's measuring apparatus registers the message ''y'' is

:<math>\operatorname{Tr}\; (\Phi_x \otimes IdI)(\omega) \cdot F_y .</math>

Therefore, to achieve the desired transmission, we require that

:<math>\operatorname{Tr}\; (\Phi_x \otimes IdI)(\omega) \cdot F_y = \delta_{xy}</math>

where ''δ_xy'' is the [[Kronecker delta]].