RT Journal Article
T1 Taming singularities of the quantum Fisher information
A1 Goldberg, Aaron Z.
A1 Romero Hervás, José Luis
A1 Sanz Ortiz, Ángel Santiago
A1 Sánchez Soto, Luis Lorenzo
AB Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of a QFIM, an immediate question is what to do with singular QFIMs. Moreover, the QFIM may be discontinuous, forcing one away from the paradigm of regular statistical models. These questions of nonregular quantum statistical models are present in both single- and multiparameter estimation. Geometrically, singular QFIMs occur when the curvature of the metric vanishes in one or more directions in the space of probability distributions, while QFIMs have discontinuities when the density matrix has parameter-dependent rank. We present a nuanced discussion of how to deal with each of these scenarios, stressing the physical implications of singular QFIMs and the ensuing ramifications for quantum metrology.
PB World Scientific Publishing Company
SN 0219-7499
YR 2021
FD 2021-12
LK https://hdl.handle.net/20.500.14352/4656
UL https://hdl.handle.net/20.500.14352/4656
LA eng
NO © 2021 World Scientific Publishing CompanyJLR, ASS, and LLSS acknowledge financial support from the European Union’s Horizon 2020 research and innovation program (Projects ApresSF and Stormytune). LLSS acknowledges funding from the Spanish Ministerio de Ciencia e Innovacion (Grant No. PGC2018-099183-B-I00).
NO Unión Europea. H2020
NO Ministerio de Ciencia e Innovación (MICINN)
DS Docta Complutense
RD 9 may 2025