= Selective quantum measurement
{title2=$\rho_i=A_i\rho A_i^\dagger/p_i$}
A selective <quantum measurement> conditions on a known outcome. For <Kraus operator> $A_i$, the <Born rule> gives $p_i=\operatorname{Tr}(A_i^\dagger A_i\rho)$ and the conditional <density operator> is $A_i\rho A_i^\dagger/p_i$ when $p_i>0$. Conditioning changes the state and can change the conditional <reduced density matrix> of a correlated remote system. That conditional state is available as such only to an observer with the outcome information.
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