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Heisenberg-Robertson's uncertainty relation expresses a limitation in thepossible preparations of the system by giving a lower bound to the product ofthe variances of two observables in terms of their commutator. Notably, it doesnot 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. Herewe give two stronger uncertainty relations, relating to the sum of variances,whose lower bound is guaranteed to be nontrivial whenever the two observablesare incompatible on the state of the system.

Stronger uncertainty relations for the sum of variances