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 …
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 …
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 …
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
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 …
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
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 …
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 …
of efforts to build a rigorous mathematical framework for quantum mechanics and other …
Pre-images of extreme points of the numerical range, and applications
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 …
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
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 …
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
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 …
continuity of a maximum-entropy inference map are discussed in the context of quantum …