Uncertainty relations beyond Heisenberg's - Arun Kumar Pati

Heisenberg-Robertson's uncertainty relation expresses a limitation in the possible preparations of the quantum system by giving a lower bound to the product of the variances of two observables in terms of their commutator. However, 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. We prove 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. The new uncertainty relations suggest that quantum world is more uncertain than what Heisenberg's relation entails.