Information geometric measures of complexity with applications to classical and quantum physical settings

C Cafaro, SA Ali - Foundations, 2021 - mdpi.com
Foundations | Free Full-Text | Information Geometric Measures of Complexity with Applications
to Classical and Quantum Physical Settings Next Article in Journal A Survey on Existence …

Numerical ranges and geometry in quantum information: Entanglement, uncertainty relations, phase transitions, and state interconversion

K Szymański - arxiv preprint arxiv:2303.07390, 2023 - arxiv.org
Studying the geometry of sets appearing in various problems of quantum information helps
in understanding different parts of the theory. It is thus worthwhile to approach quantum …

Theoretical investigations of an information geometric approach to complexity

SA Ali, C Cafaro - Reviews in Mathematical Physics, 2017 - World Scientific
It is known that statistical model selection as well as identification of dynamical equations
from available data are both very challenging tasks. Physical systems behave according to …

Signatures of quantum phase transitions from the boundary of the numerical range

IM Spitkovsky, S Weis - Journal of Mathematical Physics, 2018 - pubs.aip.org
We analyze the smoothness of the ground state energy of a one-parameter Hamiltonian by
studying the differential geometry of the numerical range and continuity of the maximum …

An information geometric perspective on the complexity of macroscopic predictions arising from incomplete information

SA Ali, C Cafaro, S Gassner… - Advances in Mathematical …, 2018 - Wiley Online Library
Motivated by the presence of deep connections among dynamical equations, experimental
data, physical systems, and statistical modeling, we report on a series of findings uncovered …

Numerical Ranges and Applications in Quantum Information

N Cao - 2021 - atrium.lib.uoguelph.ca
The numerical range (NR) of a matrix is a concept that first arose in the early 1900's as part
of efforts to build a rigorous mathematical framework for quantum mechanics and other …

Pre-images of extreme points of the numerical range, and applications

IM Spitkovsky, S Weis - arxiv preprint arxiv:1509.05676, 2015 - arxiv.org
We extend the pre-image representation of exposed points of the numerical range of a
matrix to all extreme points. With that we characterize extreme points which are multiply …

Inverse continuity of the numerical range map for Hilbert space operators

B Lins, I Spitkovsky - arxiv preprint arxiv:1810.04199, 2018 - arxiv.org
We describe continuity properties of the multivalued inverse of the numerical range map $
f_A: x\mapsto\left\langle Ax, x\right\rangle $ associated with a linear operator $ A $ defined …

A new signature of quantum phase transitions from the numerical range

IM Spitkovsky, S Weis - arxiv preprint arxiv:1703.00201, 2017 - arxiv.org
The ground state energy of a finite-dimensional one-parameter Hamiltonian and the
continuity of a maximum-entropy inference map are discussed in the context of quantum …