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

Year: 2018

Authors: Gessner M., Smerzi A.

Autors Affiliation: CNR INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy and LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: 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 Cramer-Rao bound for median-unbiased quantum phase estimation.


Volume: 97 (2)      Pages from: 022109-1  to: 022109-18

KeyWords: Cramer-Rao; entanglement; spin; distance; distributions
DOI: 10.1103/PhysRevA.97.022109

Citations: 34
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