Corollary 3, Eq. (17): minimum of two REE bounds

For all positive integers $a,b$ and every positive semidefinite trace-$1$ matrix $\rho$ on $\mathbb C^a\otimes\mathbb C^b$ whose second-party transpose $\rho^{T_2}$, defined by $\rho^{T_2}_{(i,j),(k,l)}=\rho_{(i,l),(k,j)}$, is positive semidefinite,

Here $R_\infty(\rho)=\limsup_{j\to\infty}R_{j+1}(\rho)/(j+1)$ in $[0,\infty]$, where $R_n$ is the supremum over Bell experiments on $\rho^{\otimes n}$, then over all nonnegative input distributions $p(x,y)$ summing to $1$, of the infimum over finite local boxes $Q$ of $\sum_{x,y}p(x,y)D_{\mathrm{KL},2}(P(\cdot,\cdot|x,y)\|Q(\cdot,\cdot|x,y))$. A Bell experiment applies a map in the ambient topological closure of finite LOCC maps, with positive finite local output dimensions, followed by local positive semidefinite measurement effects summing to the identity for each input of a finite scenario with positive input and output sizes; its probabilities are $P(a,b|x,y)=\operatorname{Re}\operatorname{tr}((M_{a|x}\otimes N_{b|y})L(\rho^{\otimes n}))$. Finite LOCC maps are obtained from the identity by finite recursive local Kraus measurements satisfying $\sum_iE_i^\dagger E_i=I$, branch-dependent continuation maps, and summation of branch outputs. A finite local box has the form $Q(a,b|x,y)=\sum_iw_i\mathbf1_{a=f_i(x)}\mathbf1_{b=g_i(y)}$, with nonnegative weights summing to $1$. The classical divergence is $+\infty$ when a positive numerator probability has zero denominator; otherwise it is the nonnegative truncation of $\sum_{a,b:P(a,b)>0}P(a,b)\log_2(P(a,b)/Q(a,b))$. Tensor powers multiply corresponding entries across the $n$ copies and are relabeled by finite index sets. The quantity $E_{\mathrm R}(\omega)$ is the infimum of $D_2(\omega\|\sigma)$ over all finite convex combinations $\sigma=\sum_iw_iA_i\otimes B_i$ of products of local positive semidefinite trace-$1$ matrices. This divergence is $+\infty$ unless both arguments are density matrices and $\ker\sigma\subseteq\ker\omega$; otherwise it equals $\max\{\operatorname{Re}\operatorname{tr}(\omega\log\omega-\omega\log\sigma),0\}/\log2$, with matrix functions defined by functional calculus and the real logarithm assigned value $0$ at zero. The statement includes $a=1$ or $b=1$.