Stronger Uncertainty Relations for All Incompatible Observables
Abstract
The HeisenbergRobertson 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.
 Publication:

Physical Review Letters
 Pub Date:
 December 2014
 DOI:
 10.1103/PhysRevLett.113.260401
 Bibcode:
 2014PhRvL.113z0401M
 Keywords:

 03.65.Ta;
 03.67.a;
 42.50.Lc;
 Foundations of quantum mechanics;
 measurement theory;
 Quantum information;
 Quantum fluctuations quantum noise and quantum jumps