Related papers: Analysis of SM quantum information
The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted…
The unavoidable interaction between a quantum system and the external noisy environment can be mimicked by a sequence of stochastic measurements whose outcomes are neglected. Here we investigate how this stochasticity is reflected in the…
Shannon quantum information entropies $S_{\rho,\gamma}$, Fisher informations $I_{\rho,\gamma}$, Onicescu energies $O_{\rho,\gamma}$ and complexities $e^SO$ are calculated both in position (subscript $\rho$) and momentum ($\gamma$) spaces…
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…
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…
Quantum Fisher information places the fundamental limit to the accuracy of estimating an unknown parameter. Here we shall provide the quantum Fisher information an operational meaning: a mixed state can be so prepared that a given…
A quantum measurement is Fisher symmetric if it provides uniform and maximal information on all parameters that characterize the quantum state of interest. Using (complex projective) 2-designs, we construct measurements on a pair of…
Information-based uncertainty measures like Shannon entropy, Onicescu energy and Fisher information (in position and momentum space) are employed to understand the effect of \emph{symmetric and asymmetric} confinement in a quantum harmonic…
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 prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
In the search of appropriate riemannian metrics on quantum state space the concept of statistical monotonicity, or contraction under coarse graining, has been proposed by Chentsov. The metrics with this property have been classified by…
Non-Hermitian systems have attracted considerable interest over the last few decades due to their unique spectral and dynamical properties not encountered in Hermitian counterparts. An intensely debated question is whether non-Hermitian…
Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a…
We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., $(\Delta A)^2-F_{\rm Q}[\varrho,A]/4.$ We find that it is equal to a generalized variance defined in Petz [J. Phys. A…
The Fisher-Shannon and Cramer-Rao information measures, and the LMC-like or shape complexity (i.e., the disequilibrium times the Shannon entropic power) of hydrogenic stationary states are investigated in both position and momentum spaces.…
We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized…
Statistical quantifiers are generically required to contract under physical evolutions, following the intuition that information should be lost under noisy transformations. This principle is very relevant in statistics, and it even allows…
Fisher Information is a key notion in the whole field of quantum metrology. It allows for a direct quantification of maximal achievable precision of estimation of parameters encoded in quantum states using the most general quantum…
The scaling properties of various composite information-theoretic measures (Shannon and R\'enyi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher-Shannon product and shape complexity) are studied in…
Shannon quantum information entropies $S_{x,k}$, Fisher informations $I_{x,k}$, Onicescu energies $O_{x,k}$ and statistical complexities $e^{S_{x,k}}O_{x,k}$ are calculated both in the position (subscript $x$) and momentum ($k$)…