Applying the Theory of Numerical Radius of Operators to Obtain Multi-observable Quantum Uncertainty Relations

Quantum uncertainty relations are mathematical inequalities that describe the lower bound of products of standard deviations of observables (i.e., bounded or unbounded self-adjoint operators). By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal uncertainty relation for k observables, of which the formulation depends on the even or odd quality of k. This universal uncertainty relation is tight at least for the cases k = 2 and k = 3. For two observables, the uncertainty relation is a simpler reformulation of Schrodinger's uncertainty principle, which is also tighter than Heisenberg's and Robertson's uncertainty relations.