Abstract We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information I^ (₀₁) I max ε (ρ AB) of bipartite quantum states in any dimension. The algorithm is accurate if a rank condition for marginal states within the smoothing environment is satisfied and provides an upper bound otherwise. Central to our method is a novel SDP, for which we establish primal and dual formulations and prove strong duality. With the direct application of bounding the one-shot distillable key of a quantum state, this contribution extends SDP-based techniques in quantum information theory. Thereby it improves the capabilities to compute or estimate information measures with application to various quantum information processing tasks.
Popp et al. (2026) studied this question.