Related papers: Bures Geometry of the Three-Level Quantum Systems.…
A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…
We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of…
Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…
We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…
This article contains a survey of the geometric approach to quantum correlations. We focus mainly on the geometric measures of quantum correlations based on the Bures and quantum Hellinger distances.
The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral…
Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
A general procedure is established to calculate the quantum phase diagrams for finite matter-field Hamiltonian models. The minimum energy surface associated to the different symmetries of the model is calculated as a function of the…
Various extensions to Riemann geometry have been proposed since the inception of general relativity (GR). The aim has been and continues to be to construct a quantum and dynamic spacetime that incorporates the well-known classical (static)…
A novel link between monotone metric tensors and actions of suitable extensions of the unitary group on the manifold of faithful quantum states is presented here by means of three illustrative examples related with the Bures-Helstrom metric…
The concepts of topology and geometry are of critical importance in exploring exotic phases of quantum matter. Though they have been investigated on various experimental platforms, to date a direct probe of topological and geometric…
We elucidate the Bures metric in quantum state space near a rank-changing point of the density matrix and show contrasting behavior for two-level ($N=2$) systems versus higher-level systems. Due to the smooth pure-state boundary for $N=2$,…
In many-body quantum systems, the quantum Fisher information an observer can obtain is susceptible to decoherence. Consequently, quantum enhanced metrology, such as Heisenberg scaling, cannot usually be achieved. We show, via two distinct…
The geometric properties of quantum states are crucial for understanding many physical phenomena in quantum mechanics, condensed matter physics, and optics. The central object describing these properties is the quantum geometric tensor,…
In quantum mechanics, geometry has been demonstrated as a useful tool for inferring non-classical behaviors and exotic properties of quantum systems. One standard approach to illustrate the geometry of quantum systems is to project the…
The Bures metric is a natural choice in measuring the distance of density operators representing states in quantum mechanics. In the past few years a random matrix ensemble and the corresponding joint probability density function of its…
The 3-dimensional gauge-Higgs system describes the non-perturbative infrared effects of the high-temperature phase of the Standard Model. We calculate the two-loop self-energies in the 3-dimensional SU(2) Higgs model and in the…
We define Discrete Quasi-Einstein metrics (DQE-metrics) as the critical points of discrete total curvature functional on triangulated 3-manifolds. We study DQE-metrics by introducing some combinatorial curvature flows. We prove that these…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…