Geometric Optimization for Tight Entropic Uncertainty Relations

• URL: http://arxiv.org/abs/2602.00595v1
• Date: Sat, 31 Jan 2026 08:21:17 GMT
• Title: Geometric Optimization for Tight Entropic Uncertainty Relations
• Authors: Ma-Cheng Yang, Cong-Feng Qiao,
• Abstract summary: Entropic uncertainty relations play a fundamental role in quantum information theory.<n>We recast this task as a geometric optimization problem over the quantum probability space.<n>This procedure leads to an effective outer-approximation for general measurements in finite-dimensional quantum systems with preassigned numerical precision.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Entropic uncertainty relations play a fundamental role in quantum information theory. However, determining optimal (tight) entropic uncertainty relations for general observables remains a formidable challenge and has so far been achieved only in a few special cases. Motivated by Schwonnek \emph{et al.} [PRL \textbf{119}, 170404 (2017)], we recast this task as a geometric optimization problem over the quantum probability space. This procedure leads to an effective outer-approximation method that yields tight entropic uncertainty bounds for general measurements in finite-dimensional quantum systems with preassigned numerical precision. We benchmark our approach against existing analytical and majorization-based bounds, and demonstrate its practical advantage through applications to quantum steering.

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