Experimental investigation of the stronger uncertainty relations for all incompatible observables

TL;DR

This paper experimentally verifies stronger uncertainty relations for incompatible observables, demonstrating their validity even in cases where traditional relations become trivial, thus providing a more accurate quantification of quantum incompatibility.

Contribution

The paper provides the first experimental demonstration of Maccone and Pati's stronger uncertainty relations, validating their state-dependent nontrivial bounds for incompatible observables.

Findings

Stronger uncertainty bounds are valid for incompatible observables.

Traditional Heisenberg-Robertson relation can be trivial for incompatible observables.

Experimental results agree with quantum theory predictions.

Abstract

The Heisenberg-Robertson uncertainty relation quantitatively expresses the impossibility of jointly sharp preparation of incompatible observables. However it does not capture the concept of incompatible observables because it can be trivial even for two incompatible observables. We experimentally demonstrate the new stronger uncertainty relations proposed by Maccone and Pati [Phys. Rev. Lett. 113, 260401 (2014)] relating on that sum of variances are valid in a state-dependent manner and the lower bound is guaranteed to be nontrivial for two observables being incompatible on the state of the system being measured. The behaviour we find agrees with the predictions of quantum theory and obeys the new uncertainty relations even for the special states which trivialize Heisenberg-Robertson relation. We realize a direct measurement model and give the first experimental investigation of the strengthened relations.