Computation of the Smooth Max-Mutual Information via Semidefinite Programming

• URL: http://arxiv.org/abs/2509.07743v2
• Date: Mon, 20 Oct 2025 13:58:27 GMT
• Title: Computation of the Smooth Max-Mutual Information via Semidefinite Programming
• Authors: Christopher Popp, Tobias C. Sutter, Beatrix C. Hiesmayr,
• Abstract summary: We present an iterative algorithm for computing the quantum smooth max-mutual information $Ivarepsilon_max(rho_AB)$ of bipartite quantum states in any dimension.<n>Central to our method is a novel SDP, for which we establish primal and dual formulations and prove strong duality.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an iterative algorithm based on semidefinite programming (SDP) for computing the quantum smooth max-mutual information $I^\varepsilon_{\max}(\rho_{AB})$ 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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