Escort--Husimi distributions, Fisher information and nonextensivity

We evaluate generalized information measures constructed with Husimi distributions and connect them with the Wehrl entropy, on the one hand, and with thermal uncertainty relations, on the other one. The concept of escort distribution plays a central role in such a study. A new interpretation concerning the meaning of the nonextensivity index $q$ is thereby provided. A physical lower bound for $q$ is also established, together with a ``state equation" for $q$ that transforms the escort-Cramer--Rao bound into a thermal uncertainty relation.Comment: Physics Letters A (2004), in pres

The best Fisher is upstream: data processing inequalities for quantum metrology

We apply the classical data processing inequality to quantum metrology to show that manipulating the classical information from a quantum measurement cannot aid in the estimation of parameters encoded in quantum states. We further derive a quantum data processing inequality to show that coherent manipulation of quantum data also cannot improve the precision in estimation. In addition, we comment on the assumptions necessary to arrive at these inequalities and how they might be avoided providing insights into enhancement procedures which are not provably wrong.Comment: Comments encourage

Fisher information, Wehrl entropy, and Landau Diamagnetism

Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is shown that such a problem can be "translated" into that of the thermal harmonic oscillator. We discover a new Fisher-uncertainty relation, derived via the Cramer-Rao inequality, that involves phase space localization and energy fluctuations.Comment: no figures. Physical Review B (2005) in pres

Cramer–Rao lower bounds for change points in additive and multiplicative noise

The paper addresses the problem of determining the Cramer–Rao lower bounds (CRLBs) for noise and change-point parameters, for steplike signals corrupted by multiplicative and/or additive white noise. Closed-form expressions for the signal and noise CRLBs are first derived for an ideal step with a known change point. For an unknown change-point, the noise-free signal is modeled by a sigmoidal function parametrized by location and step rise parameters. The noise and step change CRLBs corresponding to this model are shown to be well approximated by the more tractable expressions derived for a known change-point. The paper also shows that the step location parameter is asymptotically decoupled from the other parameters, which allows us to derive simple CRLBs for the step location. These bounds are then compared with the corresponding mean square errors of the maximum likelihood estimators in the pure multiplicative case. The comparison illustrates convergence and efficiency of the ML estimator. An extension to colored multiplicative noise is also discussed

Exact Conditional and Unconditional Cram\`er-Rao Bounds for Near Field Localization

This paper considers the Cram\`er-Rao lower Bound (CRB) for the source localization problem in the near field. More specifically, we use the exact expression of the delay parameter for the CRB derivation and show how this exact CRB can be significantly different from the one given in the literature and based on an approximate time delay expression (usually considered in the Fresnel region). This CRB derivation is then generalized by considering the exact expression of the received power profile (i.e., variable gain case) which, to our best knowledge, has been ignored in the literature. Finally, we exploit the CRB expression to introduce the new concept of Near Field Localization (NFL) region for a target localization performance associated to the application at hand. We illustrate the usefulness of the proposed CRB derivation and its developments as well as the NFL region concept through numerical simulations in different scenarios

Quantum criticality as a resource for quantum estimation

We address quantum critical systems as a resource in quantum estimation and derive the ultimate quantum limits to the precision of any estimator of the coupling parameters. In particular, if L denotes the size of a system and \lambda is the relevant coupling parameters driving a quantum phase transition, we show that a precision improvement of order 1/L may be achieved in the estimation of \lambda at the critical point compared to the non-critical case. We show that analogue results hold for temperature estimation in classical phase transitions. Results are illustrated by means of a specific example involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a specific exampl