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Fisher information and the complex nature of the Schr�dinger wave equation

B. Roy Frieden

Foundations of PhysicsJul 1, 199118 citations

Information in Scattered Light: From optical cooling to Fisher-information flow and decoherence

Jakob Hüpfl

Sep 1, 20260 citations

Wave-like equations obeyed by information measures

B. Roy Frieden

Familiar information measures such as due to Shannon, Kullback, etc., may be related to one basic information measure called the characteristic information I. The latter is the trace of the Fisher information matrix. The relation is a Poisson equation with I as the driving force. Thus, for small-uncertainty cases, given I all these other information measures can be generated as solutions to a Poisson equation. If one of the parameters of the system is time- like, the Poisson equation becomes a wave equation, and the information may be said to `flow.'Familiar information measures such as due to Shannon, Kullback, etc., may be related to one basic information measure called the characteristic information I. The latter is the trace of the Fisher information matrix. The relation is a Poisson equation with I as the driving force. Thus, for small-uncertainty cases, given I all these other information measures can be generated as solutions to a Poisson equation. If one of the parameters of the system is time- like, the Poisson equation becomes a wave equation, and the information may be said to `flow.'

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIENov 1, 19930 citations

Uncertainty relations from Fisher information

Z. Hradil, Jaroslav Řeháček

Journal of Modern OpticsMay 1, 20044 citations

Dirac Equation and Fisher Information

Asher Yahalom A

Previously, it was shown that Schrödinger's theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli's theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero vorticity. Here, we use the recent relativistic flow Lagrangian to represent Dirac's theory with the addition of a Lorentz invariant Fisher information term as is required by quantum mechanics.

EntropyNov 12, 20241 citation

Lie Algebraic Approach to the Fisher Information Contents

Yu Watanabe

Springer thesesDec 17, 20130 citations

Continuity equation for the flow of Fisher information in wave scattering

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