Fisher-information-based optimization of programmable optical front ends in situ generally requires a response model or parameter-labeled measurements. We show that natural parameter fluctuations can instead provide the training signal. We construct proxies for the Fisher information (FI) of one parameter and the prior-weighted FI spectrum of multiple parameters from measured covariances after subtracting conditional detection noise, assuming locally affine responses. We use simulated photon counts from two incoherent point sources to train a mode sorter that approaches the quantum limit for separation and the Nagaoka--Hayashi single-copy bound for joint centroid--separation estimation. We demonstrate count-only updates that require no instrument response model and achieve performance comparable to model-based gradients. Our results provide a route to adaptive optical measurements without controlled parameter scans.Fisher-information-based optimization of programmable optical front ends in situ generally requires a response model or parameter-labeled measurements. We show that natural parameter fluctuations can instead provide the training signal. We construct proxies for the Fisher information (FI) of one parameter and the prior-weighted FI spectrum of multiple parameters from measured covariances after subtracting conditional detection noise, assuming locally affine responses. We use simulated photon counts from two incoherent point sources to train a mode sorter that approaches the quantum limit for separation and the Nagaoka--Hayashi single-copy bound for joint centroid--separation estimation. We demonstrate count-only updates that require no instrument response model and achieve performance comparable to model-based gradients. Our results provide a route to adaptive optical measurements without controlled parameter scans.

physics.opticsCross-listedarXiv:2609.24915Sep 22, 20260 citations

Relations between parameters of a decoherent system and Fisher information

B. Roy Frieden

Fisher information (FI) is normally developed and applied within the context of classical mathematical statistics. Here we show that it alternatively arises as physical properties of a generally decoherent system. Two kinds of Fisher information are treated: the classical FI $I[p]$ and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function $\ensuremath{\rho}{(x,x}^{\ensuremath{'}}),$ the two-point coherence function $\ensuremath{\tau}(\ensuremath{\Delta}x),$ the entropy of fluctuation $H(\ensuremath{\Delta}x),$ and the cross entropy ${H}_{\mathrm{KL}}(\ensuremath{\rho}{/r}_{\ensuremath{\Delta}})$ between the system probability density function $\ensuremath{\rho}(x,x)$ and its shifted version $\ensuremath{\rho}(x+\ensuremath{\Delta}x,x+\ensuremath{\Delta}x).$Fisher information (FI) is normally developed and applied within the context of classical mathematical statistics. Here we show that it alternatively arises as physical properties of a generally decoherent system. Two kinds of Fisher information are treated: the classical FI $I[p]$ and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function $\ensuremath{\rho}{(x,x}^{\ensuremath{'}}),$ the two-point coherence function $\ensuremath{\tau}(\ensuremath{\Delta}x),$ the entropy of fluctuation $H(\ensuremath{\Delta}x),$ and the cross entropy ${H}_{\mathrm{KL}}(\ensuremath{\rho}{/r}_{\ensuremath{\Delta}})$ between the system probability density function $\ensuremath{\rho}(x,x)$ and its shifted version $\ensuremath{\rho}(x+\ensuremath{\Delta}x,x+\ensuremath{\Delta}x).$

Physical Review AAug 12, 200210 citations

Phase space view of quantum mechanical systems and Fisher information

Ágnes Nagy

Physics Letters AMay 7, 20163 citations

Epistemic Signatures of Fisher Information in Finite Fermions Systems

Angelo Plastino, Victoria Vampa

Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In this work, we provide what is, to our knowledge, the first explicit realization of the epistemic-to-physical transition of Fisher information within a finite interacting quantum system. Specifically, we analyze a model of N fermions occupying two degenerate levels and coupled by a spin-flip interaction of strength V, treated in the grand canonical ensemble at inverse temperature β. We compute the Fisher information FN(V) associated with the sensitivity of the thermal state to changes in V, and show that it becomes an observer-independent, experimentally meaningful quantity: it encodes fluctuations, tracks entropy variations, and reveals structural transitions induced by interactions. Our findings thus demonstrate that Fisher information, originally conceived as an inferential and epistemic measure, can operate as a bona fide thermodynamic observable in quantum many-body physics, bridging the gap between information-theoretic foundations and measurable physical law.Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In this work, we provide what is, to our knowledge, the first explicit realization of the epistemic-to-physical transition of Fisher information within a finite interacting quantum system. Specifically, we analyze a model of N fermions occupying two degenerate levels and coupled by a spin-flip interaction of strength V, treated in the grand canonical ensemble at inverse temperature β. We compute the Fisher information FN(V) associated with the sensitivity of the thermal state to changes in V, and show that it becomes an observer-independent, experimentally meaningful quantity: it encodes fluctuations, tracks entropy variations, and reveals structural transitions induced by interactions. Our findings thus demonstrate that Fisher information, originally conceived as an inferential and epistemic measure, can operate as a bona fide thermodynamic observable in quantum many-body physics, bridging the gap between information-theoretic foundations and measurable physical law.

Quantum ReportsOct 14, 20251 citation

Fisher information of complete quantum measurements

Anonymous, Jukka Kiukas, Daniel Klaus Burgarth +1 more

Physical Review AJul 27, 20260 citations

I[p]

and the FI channel capacity 〈I〉. These are shown to be linearly related to the partition function Z, the coherence function $\ensuremath{\rho}{(x,x}^{\ensuremath{'}}),$ the two-point coherence function $\ensuremath{\tau}(\ensuremath{\Delta}x),$ the entropy of fluctuation $H(\ensuremath{\Delta}x),$ and the cross entropy ${H}_{\mathrm{KL}}(\ensuremath{\rho}{/r}_{\ensuremath{\Delta}})$ between the system probability density function $\ensuremath{\rho}(x,x)$ and its shifted version $\ensuremath{\rho}(x+\ensuremath{\Delta}x,x+\ensuremath{\Delta}x).$