bibkey: alipour2015extended
authors: S. Alipour, A. T. Rezakhani
year: 2015
title: 'Quantum Metrology: Extended Convexity of Quantum Fisher Information'
doi: 10.1103/PhysRevA.91.042104
url: https://arxiv.org/abs/1403.8033v2
claim: Equation (4) bounds SLD quantum Fisher information of a parameter-dependent mixture by the weighted component information plus the classical Fisher information of its mixing probabilities.
strata_touched: []
license: citation-only
triage: anchor

Parameter-dependent mixtures and SLD information

The cited preprint is arXiv:1403.8033v2, dated 13 November 2014; the journal version is Physical Review A 91, 042104 (2015). Equation (4) is the extended convexity inequality. Its classical term is essential when the mixing probabilities depend on the parameter; ordinary convexity alone would omit that preparation cost. The derivation around equation (5) uses the block SLD obtained by adding the logarithmic probability derivative.

Quantum-volume §215.3 uses this established inequality as an intermediate tool. A temporary orthogonal preparation label supplies the upper bound; the actual mixture remains in the original shared program space. At zero weights the manuscript checks the state and derivative directly: its cubic amplitude zeros make both the zero block and its derivative vanish, and also make the amplitude derivative zero. It does not import a continuous Bures extension as the pointwise SLD value.

The source does not supply the channel-specific original-dimension spectral necessity, the simultaneous sharp-calibration construction, its exact minimal support dimension, or its capacity transition. Those conclusions require the additional proofs in §§213–215.

Locator

Journal DOI: 10.1103/PhysRevA.91.042104. Stable preprint URL: https://arxiv.org/abs/1403.8033v2.