Selective quantum measurement (${\rho }_i=A_i\rho A_i^{†}/p_i$)

A selective measurement in quantum mechanics conditions on a known outcome. For Kraus operator $A_i$, the Born rule gives $p_i=\mathrm{Tr}(A_i^{†}{A}_i\rho )$ and the conditional density operator is $A_i\rho A_i^{†}/p_i$ 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.