Non-convergence of the cluster expansion for conditional mutual information

Let $\rho_\beta$ be a reduced density matrix on a subsystem, and consider the cluster-expansion method applied to the logarithm of reduced density matrices in order to compute conditional mutual information. Non-convergence of the cluster expansion for conditional mutual information. At any fixed nonzero temperature, the cluster expansion method is not absolutely convergent for the conditional mutual information. This conjecture reflects a proposed inherent limitation of the method, motivated by similarities with divergence problems in the Baker–Campbell–Hausdorff expansion; it concerns the method rather than asserting that conditional mutual information itself fails to decay.