Related papers: Highly symmetric lines
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…
We introduce certain lattice sums associated with hyperplane arrangements, which are (multiple) sums running over integers, and can be regarded as generalizations of certain linear combinations of zeta-functions of root systems. We also…
For any symmetry group $H$ and any appropriate matrix dilation we give an explicit method for the construction of $H$-symmetric refinable interpolatory refinable masks which satisfy sum rule of arbitrary order $n$. For each such mask we…
We consider the problem of rescaling the lengths of a finite frame thereby transforming it into a tight one. Such frames are called scalable and have received a lot of attention in recent years. In this note we investigate the question in…
Generalized symmetries often appear in the form of emergent symmetries in low energy effective descriptions of quantum many-body systems. Non-invertible symmetries are a particularly exotic class of generalized symmetries, in that they are…
The Minimal Supersymmetric Standard Model (MSSM) can include two soft breaking terms which are often neglected: a non-analytic scalar trilinear coupling and a Higgsino bilinear term. A set of high-scale boundary conditions consistent with…
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…
The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-definable in a basic similarity type with a binary operator…
We apply the semidefinite programming approach developed in arxiv:math.MG/0608426 to obtain new upper bounds for codes in spherical caps. We compute new upper bounds for the one-sided kissing number in several dimensions where we in…
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework…
We introduce a sub-symmetry of a differential system as an infinitesimal transformation of a subset of the system that leaves the subset invariant on the solution set of the entire system. We discuss the geometrical meaning and properties…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
We present a comprehensive construction of scalar, vector and tensor harmonics on maximally symmetric three-dimensional spaces. Our formalism relies on the introduction of spin-weighted spherical harmonics and a generalized helicity basis…
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…
Harmonic frames of prime order are investigated. The primary focus is the enumeration of inequivalent harmonic frames, with the exact number given by a recursive formula. The key to this result is a one-to-one correspondence developed…