Taming singularities of the quantum Fisher information



Downloads per month over past year

Goldberg, Aaron Z. and Romero, José L. and Sanz Ortiz, Ángel Santiago and Sánchez Soto, Luis Lorenzo (2021) Taming singularities of the quantum Fisher information. International journal of quantum information, 19 (8). ISSN 0219-7499

[thumbnail of SanchezSotoLL 45 PrePRINT.pdf]

Official URL: http://dx.doi.org/10.1142/S0219749921400049


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.

Item Type:Article
Additional Information:

© 2021 World Scientific Publishing Company
JLR, 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).

Uncontrolled Keywords:Statistical distance
Subjects:Sciences > Physics > Optics
ID Code:69794
Deposited On:01 Feb 2022 19:22
Last Modified:02 Feb 2022 10:01

Origin of downloads

Repository Staff Only: item control page