Uncertainty relations for any multi observables

Abstract

Uncertainty relations describe the lower bound of product of standard deviations of observables. By revealing a connection between standard deviations of quantum observables and numerical radius of operators, we establish a universal uncertainty relation for any $k$ 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 $k=2n$ and $k=3$. For two observables, the uncertainty relation is exactly a simpler reformulation of Schrödinger's uncertainty principle.

16 pages

References in corpus (4)

• The Uncertainty Principle in the Presence of Quantum Memory
• Stronger uncertainty relations for the sum of variances
• Experimental investigation of the uncertainty principle in the presence of quantum memory
• Heisenberg Uncertainty Relation for Three Canonical Observables