Related papers: Equiangular lines, mutually unbiased bases, and sp…
We provide a class of entanglement witnesses constructed in terms of Mutually Unbiased Bases (MUBs). This construction reproduces many well-known examples like the celebrated reduction map and Choi map together with its generalizations. We…
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
Across scientific domains, a fundamental challenge is to characterize and compute the mappings from underlying physical processes to observed signals and measurements. While nonlinear neural networks have achieved considerable success, they…
In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…
We present an alternative formalism for modeling spin. The ontological elements of this formalism are base-2 sequences of length $n$. The machinery necessary to model physics is then developed by considering correlations between base-2…
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…
We present a construction for complementary pairs of arrays that exploits a set of mutually-unbiased bases, and enumerate these arrays as well as the corresponding set of complementary sequences obtained from the arrays by projection. We…
We study $k$-positive linear maps on matrix algebras and address two problems, (i) characterizations of $k$-positivity and (ii) generation of non-decomposable $k$-positive maps. On the characterization side, we derive optimization-based…
In this paper we investigate the possible supersymmetric extensions for the massive (bi)gravity theories in the lowest non-trivial order. For this purpose we construct the cubic interaction vertices for massive spin-2 and one or two massive…
Unitary error bases generalize the Pauli matrices to higher dimensional systems. Two basic constructions of unitary error bases are known: An algebraic construction by Knill, which yields nice error bases, and a combinatorial construction…
This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…
Given a metric space $(X,d)$, a set $S\subseteq X$ is called a $k$-\emph{metric generator} for $X$ if any pair of different points of $X$ is distinguished by at least $k$ elements of $S$. A $k$-\emph{metric basis} is a $k$-metric generator…
This paper is an extension of our last 1D, N = 4 supersymmetric SYK paper [arXiv:2103.11899]. In this paper we introduced the complex linear supermultiplet (CLS), which is "usefully inequivalent" to the chiral supermultiplet. We construct…
Let $R$ be a finite commutative ring with unity $1_R$ and $k \in R$. Properties of one-sided $k$-orthogonal $n \times n$ matrices over $R$ are presented. When $k$ is idempotent, these matrices form a semigroup structure. Consequently new…
We consider real and complex equiangular lines, generated by unit vectors. We show that, for an arbitrary dimension $d$, if there exists a set of $d^2$ equiangular unit vectors in $\mathbb{C}^d$, then there must exist a set of $d^2$…
We present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and…
In this paper we study plus-one generated arrangements of conics and lines in the complex projective plane with simple singularities. We provide several degree-wise classification results that allow us to construct explicit examples of such…
Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin…
For nonlinear sigma-models in the unitary symmetry class, the non-linear target space can be parameterized with cubic polynomials. This choice of coordinates has been known previously as the Dyson-Maleev parameterization for spin systems,…
Let $d$ be a positive fundamental discriminant, and let $\mathcal{C}_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$. For each $K \in \mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with…