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

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

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity