Answer by glS for How does the Kraus decomposition imply the Stinespring...
There's no need to increase the dimension of $\newcommand{\calH}{{\mathcal H}}\calH_E$ to $D+1$. All you care about is that $U$ must send orthonormal vectors to orthonormal vectors. What the state...
View ArticleHow does the Kraus decomposition imply the Stinespring representation?
To show that the Kraus decomposition $\Phi(\rho)=\sum_{k=1}^D M_k\rho_S M_k^\dagger$ implies the Stinespring form $$\Phi(\rho)=\text{tr}_E[U_{SE}(\rho_S\otimes|0\rangle\langle 0|_E)U_{SE}^\dagger]$$ we...
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