Sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. Their consequences are, in particular, inequalities, giving nonzero lower bounds for the products of two variances in the case of zero mean value of the commutator between the related operators. Explicit examples show that the bounds can be better than the known Robertson-Schrödinger one.

• Received 27 October 2017
• Revised 30 December 2017

DOI:https://doi.org/10.1103/PhysRevA.97.022105