Optimal Uncertainty Relations for a Single Observable

arXiv:2605.26331 · quant-ph, math-ph, math.MP · Submitted 2026-05-25 · Read on arXiv

quant-ph, math-ph, math.MP

Submitted: 2026-05-25

Updated: 2026-09-24

Comments: 34 pages, 1 figure; substantially revised and expanded in V2, with stronger connections to quantum Fisher information and related previous work; reformatted for submission to Quantum; comments are welcome

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Fisher Information — 15× in this paper · explained in 3 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Generalization — 2× in this paper · explained in 13 episodes
• Conservation Laws — 1× in this paper · explained in 3 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes

Sources

• About Heisenberg Uncertainty Relation (by E.Schrodinger)
• Beyond Robertson-Schr"odinger: A General Uncertainty Relation Unveiling Hidden Noncommutative Trade-offs
• Coherence-variance uncertainty relation and coherence cost for quantum measurement under conservation laws
• Quantum Fisher Information as the Convex Roof of Variance

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