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The Identification of Mean Quantum Potential with Fisher Information Leads to a Strong Uncertainty Relation

Yakov Bloch, Eliahu Cohen

arXiv:2210.07732Foundations of PhysicsOct 29, 20224 citations

Quantum Fisher Information and Uncertainty Relations

Shunlong Luo

Letters in Mathematical PhysicsAug 1, 200094 citations

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Abdallah Slaoui, Bakmou Lahcen, Mohammed Daoud A +1 more

arXiv:1904.12132Physics Letters AApr 26, 201972 citations

On Covariance and Quantum Fisher Information

Shunlong Luo

For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.For a quantum state and a set of observables, we can construct an associated covariance matrix and a natural quantum Fisher information matrix. These two matrices characterize the uncertainty and information content of the observables in the relevant state. An inequality between these two matrices is established. This inequality may be interpreted as a general quantification of the Heisenberg uncertainty principle from a statistical estimation perspective. In particular, it implies a new uncertainty relation which refines the celebrated Schrödinger uncertainty relation.

Theory of Probability and Its ApplicationsJan 1, 20092 citations

Uncertainty principle and quantum Fisher information

Paolo Gibilisco, Tommaso Isola

arXiv:math-ph/0509046Annals of the Institute of Statistical MathematicsDec 29, 200649 citations

Uncertainty Relations in Terms of Fisher Information

Luo Shun-Long

By virtue of the well-known concept of Fisher information in the theory of statistical inference, we obtain an inequality chain which generalizes and refines the conventional Heisenberg uncertainty relations.

Communications in Theoretical PhysicsSep 15, 20015 citations

On a refinement of Heisenberg uncertainty relation by means of quantum Fisher information

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