Uncertainty principle with quantum Fisher information

2007/07/31 by Attila Andai · 1 citation
Physics and Astronomy · Mathematics · #math-ph #math.MP #msc:62B10 #msc:94A17

paper · pdf · doi:10.1063/1.2830429

published as Journal of Mathematical Physics, 49, 012106, 2008. · 8 pages, LaTeX; added references

arxiv created 2007/10/11 · arxiv updated 2009/12/01

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.

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