The Optimal Uncertainty Relation

Abstract

Employing the lattice theory on majorization, we investigate the universal quantum uncertainty relation for any number observables and general measurement. We find: 1. The least bounds of the universal uncertainty relations can only be properly defined in the lattice theory; 2. Contrary to variance and entropy, the metric induced by the majorization lattice implies an intrinsic structure of the quantum uncertainty; 3. The lattice theory correlates the optimization of uncertainty relation with the entanglement transformation under local quantum operation and classical communication. Interestingly, the optimality of the universal uncertainty relation is found can be mimicked by the Lorenz curve, initially introduced in economics to measure the wealth concentration degree of a society.

25 pages, 2 figures; published in Ann. Phys. (Berlin)

References in corpus (6)

• State-independent Uncertainty Relations and Entanglement Detection in Noisy Systems
• Tight entropic uncertainty relations for systems with dimension three to five
• Majorization uncertainty relations for mixed quantum states
• Approximate transformations of bipartite pure-state entanglement from the majorization lattice
• State-independent Uncertainty Relations and Entanglement Detection
• Optimal Universal Uncertainty Relations

Cited by in corpus (16)

• Tight $N$-observable uncertainty relations and their experimental demonstrations
• The Generalized Uncertainty Principle
• Optimal common resource in majorization-based resource theories
• The Uncertainty Principle of Quantum Processes
• Generalized Wigner-Yanase Skew Information and the Affiliated Inequality
• Uncertainty relations based on Wigner-Yanase skew information
• Experimental investigation of the uncertainty relations with coherent light
• Extremal elements of a sublattice of the majorization lattice and approximate majorization
• An Effective Way of Characterizing the Quantum Nonlocality
• Quantum Uncertainty Equalities and Inequalities for Unitary Operators
• Experimental test of the majorization uncertainty relation with mixed states
• An optimal measurement strategy to beat the quantum uncertainty in correlated system
• Characterizing the Quantum Non-locality by the Mathematics of Magic Square
• A Universal Quantum Certainty Relation for Arbitrary Number of Observables
• Probabilistic Coherence Transformation Under Strictly Incoherent Operation
• Witness High-Dimensional Quantum Steering via Majorization Lattice