Related papers: On a conjecture regarding Fisher information
We review the introduction of likelihood functions and Fisher information in classical estimation theory, and we show how they can be defined in a very similar manner within quantum measurement theory. We show that the stochastic master…
Using the transport-of-intensity approach for free-space optical propagation in the paraxial regime, we show that diffraction is fundamentally related to the Fisher information associated with models of the transverse intensity…
Classically, Fisher information is the relevant object in defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, there is no notion of design optimality…
Local information objectivity, that local, independent observers can infer the same information about a model upon exchange of independently acquired experimental data, is fundamental to science. It is mathematically encoded via Cencov's…
We show that an information theoretic distance measured by the relative Fisher information between canonical equilibrium phase densities corresponding to forward and backward processes is intimately related to the gradient of the dissipated…
Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on…
In this paper we study the Fisher information metric on the space of the coupling constants on both sides of the duality between non-relativistic dipole field theories and string theory in Schr\"odinger spacetime. We consider the following…
We show how Fisher's information already known particular character as the fundamental information geometric object which plays the role of a metric tensor for a statistical differential manifold, can be derived in a relatively easy manner…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
Results by van der Vaart (1991) from semi-parametric statistics about the existence of a non-zero Fisher information are reviewed in an infinite-dimensional non-linear Gaussian regression setting. Information-theoretically optimal inference…
Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, in a state $\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not…
Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold…
The half-line one-dimensional Coulomb potential is possibly the simplest D-dimensional model with physical solutions which has been proved to be successful to describe the behaviour of Rydberg atoms in external fields and the dynamics of…
Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…
We consider the impact that temporal correlations in the measurement statistics can have on the achievable precision in a sequential metrological protocol. In this setting, and for a single quantum probe, we establish that it is the…
In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher's information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear)…
In this contribution, quantum Fisher information is utilized to estimate the parameters of a central qubit interacting with a single-spin qubit. The effect of the longitudinal, transverse and the rotating strengths of the magnetic field on…
Starting with the relative entropy based on a previously proposed entropy function $S_q[p]=\int dx p(x)(-\ln p(x))^q$, we find the corresponding Fisher's information measure. After function redefinition we then maximize the Fisher…