Fisher Information as a Measure of Time

B. Roy Frieden

Ágnes Nagy

The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.

Ping Chen, Shunlong Luo

Tzu-Chao Hung

Fisher information measures a disorder system, which is specified by a corresponding probability, the likelihood. In this article, we provide a bridge to connect classical and quantum mechanics by using Fisher information. Following the principle of minimum Fisher information, we can derive the time-dependent Schrodinger equation step by step.

Z. Hradil, Jaroslav Řeháček

Bram Verreussel, Jacob Seifert, Allard P. Mosk

In metrology, Fisher information is an important metric that quantifies the precision that can be achieved in a measurement. For optical measurements using coherent light it has been shown that Fisher information can be expressed simply using the scattering matrix of the system. Fisher information can be maximized over the input modes to achieve maximum information states, which produce optimally precise estimates for a parameter when the system is limited by photon noise. Here, we extend this approach to multiparameter estimation, in which case Fisher information takes the form of a matrix. We consider several scalar functions of the Fisher matrix to optimize the precision in multiple parameters at the same time. We also consider strategies for dealing with nuisance parameters, which can degrade the achievable precision of other parameters but are not of interest to measure. We corroborate our findings numerically using a scattering system of 2D coupled dipoles.