Stronger uncertainty relations for the sum of variances

TL;DR

This paper introduces two stronger uncertainty relations based on the sum of variances, providing guaranteed nontrivial bounds for incompatible observables, improving upon traditional Heisenberg-Robertson relations.

Contribution

The authors present novel uncertainty relations for the sum of variances that ensure nontrivial bounds for incompatible observables, addressing limitations of previous formulations.

Findings

New uncertainty relations with guaranteed nontrivial bounds

Applicable to incompatible observables in quantum systems

Improves the understanding of quantum measurement limitations

Abstract

Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the system by giving a lower bound to the product of the variances of two observables in terms of their commutator. Notably, it does not capture the concept of incompatible observables because it can be trivial, i.e., the lower bound can be null even for two non-compatible observables. Here we give two stronger uncertainty relations, relating to the sum of variances, whose lower bound is guaranteed to be nontrivial whenever the two observables are incompatible on the state of the system.