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Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More precisely, for a completely positive map $\\Omega:L(B')\\to L(A)$, we consider the quantity $\\upsilon_p(\\Omega)$ defined by optimizing $\\|(\\Omega\\otimes \\mathrm{id}_E)(\\sigma^{B'E})\\|_p$ over all bipartite states $\\sigma^{B'E}$ whose $B'$-marginal is maximally mixed. We focus on the case $p=2$. 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Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More precisely, for a completely positive map $\\Omega:L(B')\\to L(A)$, we consider the quantity $\\upsilon_p(\\Omega)$ defined by optimizing $\\|(\\Omega\\otimes \\mathrm{id}_E)(\\sigma^{B'E})\\|_p$ over all bipartite states $\\sigma^{B'E}$ whose $B'$-marginal is maximally mixed. We focus on the case $p=2$. 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