Related papers: Fundamental weight systems are quantum states
It is shown that quantum homogeneous coordinate rings of generalised flag manifolds corresponding to minuscule weights, their Schubert varieties, big cells, and determinantal varieties are AS-Cohen-Macaulay. The main ingredient in the proof…
The measurement based, or one-way, model of quantum computation for continuous variables uses a highly entangled state called a cluster state to accomplish the task of computing. Cluster states that are universal for computation are a…
Geometric aspects of physics play a crucial role in modern condensed matter physics. The quantum metric is one of these geometric quantities which defines the distance on a parameter space and contributes to various physical phenomena, such…
Quantifying quantum entanglement is a pivotal challenge in quantum information science, particularly for high-dimensional systems, due to its computational complexity. This thesis extends the geometric measure of entanglement (GME) to…
Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the…
In this paper we study the quantum phase properties of {\it "nonlinear coherent states"} and {\it "solvable quantum systems with discrete spectra"} using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
A $G-$family of quandles is an algebraic construction which was proposed by A. Ishii, M. Iwakiri, Y. Jang, K. Oshiro in 2013. The axioms of these algebraic systems were motivated by handlebody-knot theory. In the present work we investigate…
The geometric measure of entanglement of variational quantum states is studied on the basis of its relation with the mean value of spin. We examine n-qubit quantum states prepared by a variational circuit with a layer formed by the…
The consistent embedding of Loop Quantum Gravity (LQG) effects within the Standard Model requires a rigorous understanding of how Planck-scale deformations manifest at low energies. While phenomenological approaches often introduce…
We report the existence of confined massless fermion states in a graphene quantum well (QW) by means of analytical and numerical calculations. These states show an unusual quasi-linear dependence on the momentum parallel to the QW: their…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
This paper presents a geometrical analysis of finite length XY quantum chains. We begin by examining the ground state and the first excited state of the model, emphasizing the impact of finite size effects under two distinct choices of the…
The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. GHWs are of great interest in many applications since they convey detailed information of linear codes. In this paper, we continue the work of [10] to study…
The critical theories for the topological phase transitions of integer quantum Hall states to a trivial insulating state with the same symmetry can be obtained by calculating the ground state entanglement spectrum under a symmetric…
We formulate a local picture of strongly correlated systems as a Feynman sum over atomic configurations. The hopping amplitudes between these atomic configurations are identified as the renormalization group charges, which describe the…
Gravitational radiation from known astrophysical sources is conventionally treated classically. This treatment corresponds, implicitly, to the hypothesis that a particular class of quantum-mechanical states -- the so-called coherent states…
Pairwise quantum correlations in the ground state of a N-spins antiferromagnetic chain described by the Heisenberg model with nearest neighbor exchange coupling are investigated. By varying a single coupling between two neighboring sites it…
We present quantum holonomy theory, which is a non-perturbative theory of quantum gravity coupled to fermionic degrees of freedom. The theory is based on a C*-algebra that involves holonomy-diffeomorphisms on a 3-dimensional manifold and…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…