This article is cited in 2 papers

Short Communications

On Covariance and Quantum Fisher Information

S. Luo

Academy of Mathematics and Systems Science

Abstract: 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.

Keywords: covariance, quantum Fisher information, uncertainty relations, determinant.

Received: 14.11.2005
Revised: 06.06.2007

Language: English

DOI: 10.4213/tvp2423

 English version: Theory of Probability and its Applications, 2009, 53:2, 329–334

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