Related papers: Information geometry, dynamics and discrete quantu…
We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…
We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension…
Recent advancements have revealed new links between information geometry and classical stochastic thermodynamics, particularly through the Fisher information (FI) with respect to time. Recognizing the non-uniqueness of the quantum Fisher…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
The quantum phase diagram for a finite $3$-level system in the $\Lambda$ configuration, interacting with a two-mode electromagnetic field in a cavity, is determined by means of information measures such as fidelity, fidelity susceptibility…
Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems,…
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with…
We present a discrete form of the Wheeler-DeWitt equation for quantum gravitation, based on the lattice formulation due to Regge. In this setup the infinite-dimensional manifold of 3-geometries is replaced by a space of three-dimensional…
This thesis explores important concepts in the area of quantum information geometry and their relationships. We highlight the unique characteristics of these concepts that arise from their quantum mechanical foundations and emphasize the…
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…