Optimum estimation under generalized unbiasedness

Stangenhaus, Gabriela

doi:10.31274/rtd-180813-706

Cited by 1 publication

(3 citation statements)

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“…The generalized Fisher information has been studied in the literature on statistical inference and information theory [61][62][63][64][65][66]. In Ref.…”

Section: B Classical Statistical Speed: the Generalized Fisher Informentioning

confidence: 99%

“…In these cases, alternative measures of statistical dispersion besides the variance are more natural. These alternative cost functions, in turn, lead to different analogs of the Cramér-Rao bound [62,63,106,107]; recall also the Barankin bounds which were discussed in Sec. II B 3.…”

Section: B Median-unbiased Quantum Phase Estimationmentioning

confidence: 99%

“…Based on the above reasoning, we employ the quantity 1/2g θ est (θ|θ) as a measure of dispersion for median-unbiased estimators. For any median-unbiased estimator θ est the following holds [63] (see Refs. [107,108] for further generalizations):…”

Section: B Median-unbiased Quantum Phase Estimationmentioning

confidence: 99%

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Statistical speed of quantum states: Generalized quantum Fisher information and Schatten speed

Gessner

Smerzi

2018

Phys. Rev. A

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We analyze families of measures for the quantum statistical speed which include as special cases the quantum Fisher information, the trace speed, i.e., the quantum statistical speed obtained from the trace distance, and more general quantifiers obtained from the family of Schatten norms. These measures quantify the statistical speed under generic quantum evolutions and are obtained by maximizing classical measures over all possible quantum measurements. We discuss general properties, optimal measurements and upper bounds on the speed of separable states. We further provide a physical interpretation for the trace speed by linking it to an analog of the quantum Cramér-Rao bound for median-unbiased quantum phase estimation.

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“…The generalized Fisher information has been studied in the literature on statistical inference and information theory [61][62][63][64][65][66]. In Ref.…”

Section: B Classical Statistical Speed: the Generalized Fisher Informentioning

confidence: 99%