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Link to original content: https://doi.org/10.48550/arXiv.1302.5311
[1302.5311] Quantum Fisher Information as the Convex Roof of Variance
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Quantum Physics

arXiv:1302.5311 (quant-ph)
[Submitted on 21 Feb 2013]

Title:Quantum Fisher Information as the Convex Roof of Variance

Authors:Sixia Yu
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Abstract:Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given observable has the minimal averaged variance, which equals exactly to the quantum Fisher information for estimating an unknown parameter generated by the unitary dynamics with the given observable as Hamiltonian. In particular we shall prove that the quantum Fisher information is the convex roof of the variance, as conjectured by Toth and Petz based on numerical and analytical evidences, by constructing explicitly a pure-state ensemble of the given mixed state in which the averaged variance of a given observable equals to the quantum Fisher information.
Comments: 2 Pages
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:1302.5311 [quant-ph]
  (or arXiv:1302.5311v1 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1302.5311

Submission history

From: Sixia Yu [view email]
[v1] Thu, 21 Feb 2013 15:41:51 UTC (4 KB)
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