  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.
