title: Stronger uncertainty relations for all incompatible observables.
abstract: The Heisenberg-Robertson 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 noncompatible 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.
authors.affiliation: Dipartimento Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Maccone
authors.affiliation: Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India and Department of mathematics, Zhejiang University, Hangzhou 310027, People's Republic of China.
authors.forename: Arun K
authors.initials: AK
authors.lastname: Pati