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arXiv · 2509.07743

Computation of the Smooth Max-Mutual Information via Semidefinite Programming

Christopher Popp·Tobias C. Sutter·Beatrix C. Hiesmayr
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Abstract

We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information $I^\varepsilon_{\max}(ρ_{AB})$ 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.

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Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr. 2025-10-20. Computation of the Smooth Max-Mutual Information via Semidefinite Programming. https://arxiv.org/abs/2509.07743

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