Tight $N$-observable uncertainty relations and their experimental demonstrations

TL;DR

This paper derives and experimentally verifies strong, universal uncertainty relations for multiple observables in quantum physics, demonstrating their robustness and fundamental significance.

Contribution

It introduces new tight multiplicative and additive uncertainty relations for multiple observables with experimental validation.

Findings

Experimental confirmation of the uncertainty relations in a spin-1/2 system

Demonstration of the robustness and validity of the derived bounds

Establishment of stringent lower bounds for multiple observables

Abstract

The uncertainty relation, as one of the fundamental principles of quantum physics, captures the incompatibility of noncommuting observables in the preparation of quantum states. In this work, we derive two strong and universal uncertainty relations for $N(N\ge2)$ observables with discrete and bounded spectra, one in multiplicative form and the other in additive form. To verify their validity, for illustration, we implement in the spin-1/2 system an experiment with single-photon measurement. The experimental results exhibit the validity and robustness of these uncertainty relations, and indicate the existence of stringent lower bounds.