Related papers: Information Geometry of Complex Hamiltonians and E…
A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still missing. In order to fill this gap we extend the so-called fidelity approach to quantum…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the…
To what extent do individual eigenstates encode information of their underlying Hamiltonian, and how does this depend on their spectral position? For many-body quantum systems, this issue is widely understood in terms of the differing…
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
In this paper, we report our latest research on a novel theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, an…
A well-studied scenario in quantum parameter estimation theory arises when the parameter to be estimated is imprinted on the initial state by a Hamiltonian of the form $\theta G$. For such "phase shift Hamiltonians" it has been shown that…
The Fisher Information Metric (FIM) and the associated Cram\'er-Rao Bound (CRB) are fundamental tools in statistical signal processing, which inform the efficient design of experiments and algorithms for estimating the underlying…
Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…
In this paper, we show how information geometry, the natural geometry of discrete probability distributions, can be used to derive the quantum formalism. The derivation rests upon three elementary features of quantum phenomena, namely…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is…
We present a framework for the detection and estimation of deformations applied to a grid of sources. Our formalism uses the Hamiltonian formulation of the quantum Fisher information matrix (\textsc{qfim}) as the figure of merit to quantify…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
Fine-tuning and naturalness, the sensitivity of low-energy observables to small changes in the fundamental parameters of a theory, are cornerstones of physics beyond the Standard Model. We propose a new measure of fine-tuning based on…
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…