Related papers: Remarks on Fisher information
The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction…
It is shown that calculation of the momentum Fisher information of the quasione- dimensional hydrogen atom recently presented by Saha et al (2017 Eur. J. Phys. {\bf 38} 025103) is wrong. A correct derivation is provided and its didactical…
These notes review the theory of Fisher information, especially its use in kinetic theory of gases and plasmas. The recent monotonicity theorem by Guillen--Silvestre for the Landau--Coulomb equation is put in perspective and generalised.…
We study the existence of the maximal quantum Fisher information matrix in multi-parameter quantum estimation, which bounds the ultimate precision limit. We show that when the maximal quantum Fisher information matrix exists, it can be…
We explore quantum phase transitions in the spin-1/2 $XX$ chain with three-spin interaction in terms of local quantum Fisher information and one-way quantum deficit, together with the demonstration of quantum fluctuations. Analytical…
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement…
The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially…
We investigated quantum critical behaviours in the non-equilibrium steady state of a $XXZ$ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states,…
We strengthen the connection between Information Theory and quantum-mechanical systems using a recently developed dequantization procedure whereby quantum fluctuations latent in the quantum momentum are suppressed. The dequantization…
Diffraction on the slit can be interpreted in accordance with the Heisenberg uncertainty principle. This elementary example hints at the importance of the information theory for the quantum physics. The role played by one particularly…
The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can…
We derive general upper bounds to pointwise mutual information in terms of stochastic Fisher information and show these bounds average to known results in the literature for bounds to mutual information in terms of Fisher information. These…
We derive explicit expressions for the quantum Fisher information and the symmetric logarithmic derivative (SLD) of a quantum state in the exponential form; the SLD is expressed in terms of the generator. Applications include…
This paper comments on the recently reported quantum oscillations in underdoped YBCO crystals. The implications to other experiments and some hurdles to validating the proposed interpretation are discussed.
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the…
Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials…
The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we…
Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…
Connections between Fisher information, Kaehler geometry of a quantum projective Hilbert space, and the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter are sketched.
Recently new approaches for sensing the frequency of time dependent Hamiltonians have been presented, and it was shown that the optimal Fisher information scales as $T^{4}.$ We present here our interpretation of this new scaling, where the…