Uncertainty principle with quantum Fisher information

Abstract

In this paper we prove a nontrivial lower bound for the determinant of the covariance matrix of quantum mechanical observables, which was conjectured by Gibilisco, Isola and Imparato. The lower bound is given in terms of the commutator of the state and the observables and their scalar product, which is generated by an arbitrary symmetric operator monotone function.

8 pages, LaTeX; added references

References in corpus (4)

• Metric adjusted skew information
• Uncertainty Principle and Quantum Fisher Information - II
• A volume inequality for quantum Fisher information and the uncertainty principle
• A Robertson-type Uncertainty Principle and Quantum Fisher Information

Cited by in corpus (3)

• Inequalities for quantum skew information
• Quantum covariance, quantum Fisher information and the uncertainty principle
• From quasi-entropy to skew information