= Quantum operation
{title2=$\mathcal E(\rho)=\sum_\alpha K_\alpha\rho K_\alpha^\dagger$}
{wiki}
A <completely positive map> with $\sum_\alpha K_\alpha^\dagger K_\alpha\leq I$ is a trace-nonincreasing quantum operation, representing an outcome branch with its probability retained in the trace. A deterministic <quantum channel> has equality and is trace preserving. Dividing a branch output by its trace gives a conditional state but generally produces a nonlinear update; that normalization is not part of the linear quantum operation.
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