Related papers: Super-symmetric informationally complete measureme…
This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N…
The existence problem for maximal sets of equiangular lines (or SICs) in complex Hilbert space of dimension $d$ remains largely open. In a previous publication (arXiv:2112.05552) we gave a conjectural algorithm for how to construct a SIC if…
Let $\mathcal{X}_S$ denote the class of spaces homeomorphic to two closed orientable surfaces of genus greater than one identified to each other along an essential simple closed curve in each surface. Let $\mathcal{C}_S$ denote the set of…
The rank of a hierarchically hyperbolic space is the maximal number of unbounded factors in a standard product region. For hierarchically hyperbolic groups, this coincides with the maximal dimension of a quasiflat. Examples for which the…
We introduce the spin coherence scale as a measure of quantum coherence for spin systems, generalizing the quadrature coherence scale (QCS) previously defined for quadrature observables. This SU($2$)-invariant measure quantifies the…
Enhancement of global symmetry and supersymmetry in the infrared is one of the most intriguing phenomena in quantum field theory. We investigate such phenomena in a large class of three dimensional superconformal field theories, known as…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…
The physical problem behind informationally complete (IC) measurements is determining an unknown state statistically by measurement outcomes, known as state tomography. It is of central importance in quantum information processing such as…
We study conditions under which quasi-conformal homeomorphisms are quasi-isometries. We show that if two nilpotent geodesic Lie groups are quasi-conformally homeomorphic, then they are quasi-isometrically equivalent. We also give more…
Abundant second-order maximally conformally superintegrable Hamiltonian systems are re-examined, revealing their underlying natural Weyl structure and offering a clearer geometric context for the study of St\"ackel transformations (also…
Following a brief outline of the CLIC project, this talk summarizes some of the principal motivations for an e+ e- collider with E_CM = 3 TeV. It is shown by several examples that CLIC would represent a significant step beyond the LHC and…
We compute the full isometry group of any left invariant metric on a simply connected, non-unimodular Lie group of dimension three. As an application, we determine the index of symmetry of such metrics and prove that the singularities of…
Supersymmetric gauge theories of certain class possess a large hidden nonperturbative symmetry described by the Ding-Iohara-Miki (DIM) algebra which can be used to compute their partition functions and correlators very efficiently. We lift…
The symmetry SU(2) and its geometric Bloch Sphere rendering are familiar for a qubit (spin-1/2) but extension of symmetries and geometries have been investigated far less for multiple qubits, even just a pair of them, that are central to…
We introduce a one-parameter family of transforms, $U^t_{(m)}$, $t>0$, from the Hilbert space of Clifford algebra valued square integrable functions on the $m$--dimensional sphere, $L^2(S^{m},d\sigma_{m})\otimes \mathbb{C}_{m+1}$, to the…
The space of positively curved hermitian metrics on a positive holomorphic line bundle over a compact complex manifold is an infinite-dimensional symmetric space. It is shown by Phong and Sturm that geodesics in this space can be uniformly…
We study isometric representations of product systems of correspondences over the semigroup $\mathbb{N}^k$ which are minimal dilations of finite dimensional, fully coisometric representations. We show the existence of a unique minimal…
We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, "as close as possible" to orthonormal bases for the space of quantum states. These measures are distinguished by an…
We apply dimer diagram techniques to uncover discrete global symmetries in the fields theories on D3-branes at singularities given by general orbifolds of general toric Calabi-Yau threefold singularities. The discrete symmetries are…
The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2,2)-supersymmetric systems in 2-dimensional spacetime which are closely…