**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.