Related papers: Information geometry in quantum field theory: less…
This paper is a strongly geometrical approach to the Fisher distance, which is a measure of dissimilarity between two probability distribution functions. The Fisher distance, as well as other divergence measures, are also used in many…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do…
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…
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the…
Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…
We explore the connection between two problems that have arisen independently in the signal processing and related fields: the estimation of the geometric mean of a set of symmetric positive definite (SPD) matrices and their approximate…
In order to characterize quantum states within the context of information geometry, we propose a generalization of the Gaussian model, which we called the Hermite-Gaussian model. We obtain the Fisher-Rao metric and the scalar curvature for…
Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…
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…
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…
Metric adjusted skew information, induced from quantum Fisher information, is a well-known family of resource measures in the resource theory of asymmetry. However, its asymptotic rates are not valid asymmetry monotone since it has an…
We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the AdS/CFT correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general…
We introduce a canonical decomposition of the quantum Fisher information (QFI) for centered multimode Gaussian states into two additive pieces: an even part that captures changes in the symplectic spectrum and an odd part associated with…
We introduce a method of reverse holography by which a bulk metric is shown to arise from locally computable multiscale correlations of a boundary quantum field theory (QFT). The metric is obtained from the Petz-R\'enyi mutual information…
Standard quantum metrology relies on ensemble-averaged quantities, such as the Quantum Fisher Information (QFI), which often mask the fluctuations inherent to single-shot realizations. In this work, we bridge the gap between quantum…
Holographic duals for CFTs compactified on a Riemann surface $\Sigma$ with a twist are cast in the language of wedge holography. $\Sigma$ starts as part of the field theory geometry in the UV and becomes part of the internal space in the…
We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The…
Understanding how neural population responses represent sensory information is a central problem in systems neuroscience. One approach is to define a representational geometry on stimulus space in which distances reflect how reliably…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…