On a conjecture regarding Fisher information

Abstract

Fisher's information measure plays a very important role in diverse areas of theoretical physics. The associated measures as functionals of quantum probability distributions defined in, respectively, coordinate and momentum spaces, are the protagonists of our present considerations. The product of them has been conjectured to exhibit a non trivial lower bound in [Phys. Rev. A (2000) 62 012107]. We show here that such is not the case. This is illustrated, in particular, for pure states that are solutions to the free-particle Schrödinger equation. In fact, we construct a family of counterexamples to the conjecture, corresponding to time-dependent solutions of the free-particle Schrödinger equation. We also give a new conjecture regarding any normalizable time-dependent solution of this equation.

arXiv comment4 pages; revised equations, results unchanged

References in corpus (8)

• Characterizing Nonclassical Correlations via Local Quantum Uncertainty
• Extremal properties of the variance and the quantum Fisher information
• Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
• Quantum properties of classical Fisher information
• Quantum Fisher information for density matrices with arbitrary ranks
• A Schroedinger link between non-equilibrium thermodynamics and Fisher information
• Heisenberg-Fisher thermal uncertainty measure
• Entropy and complexity properties of the d-dimensional blackbody radiation

Cited by in corpus (4)

• Quantum information measures of the one-dimensional Robin quantum well
• Statistical Analysis and Information Theory of Screened Kratzer-Hellmann Potential Model
• Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
• Information theoretic measures on quantum droplets in ultracold atomic systems