Related papers: Qudits of composite dimension, mutually unbiased b…
We survey the operator algebras arising as commutants modulo normed ideals of finite sets of hermitian operators and connections to perturbations of operators and noncommutative geometry.
In this paper we discuss the relationship between noninvertible topological operators, one-form symmetries, and decomposition of two-dimensional quantum field theories, focusing on two-dimensional orbifolds with and without discrete…
We consider three kinds of quotients of the curve complex which are obtained by coning off uniformly quasi-convex subspaces: symmetric curve sets, non-maximal train track sets, and compression body disc sets. We show that the actions of the…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
We develop a strong connection between maximally commuting bases of orthogonal unitary matrices and mutually unbiased bases. A necessary condition of the existence of mutually unbiased bases for any finite dimension is obtained. Then a…
The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel…
By solving a problem regarding polynomials in a quotient ring, we obtain the relative hull and the Hermitian hull of projective Reed-Muller codes over the projective plane. The dimension of the hull determines the minimum number of…
In this paper we give explicit formulas for higher order differential operators on a finitely generated projective module $E$ on an arbitrary commutative unital ring $A$. We use the differential operators constructed to give a simple…
Commutative complex numbers of the form u=x+\alpha y+\beta z+\gamma t in 4 dimensions are studied, the variables x, y, z and t being real numbers. Four distinct types of multiplication rules for the complex bases \alpha, \beta and \gamma…
The geometry of cosets in the subgroups H of the two-generator free group G =\textless{} a, b \textgreater{} nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. Dessins stabilize…
Lorentz invariant quantum field theories (QFTs) with fermions in four spacetime dimensions (4D) have a $\mathbb{Z}_4$ symmetry provided there exists a basis of operators in the QFT where all operators have even operator dimension, $d$,…
*This paper is from 2018* In this paper, we try to classify moduli spaces of arrangements of $12$ lines with sextic points. We show that moduli spaces of arrangements of $12$ lines with sextic points can consist of more than two connected…
A higher level analog of Weyl modules over multi-variable currents is proposed. It is shown that the sum of their dual spaces form a commutative algebra. The structure of these modules and the geometry of the projective spectrum of this…
We study the representation and visualization of finite-dimensional quantum systems. In a generalized Wigner representation, multi-spin operators can be decomposed into a symmetry-adapted tensor basis and they are mapped to multiple…
We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…
For a wide variety of quantum potentials, including the textbook `instanton' examples of the periodic cosine and symmetric double-well potentials, the perturbative data coming from fluctuations about the vacuum saddle encodes all…
It is shown that two vectors with coordinates in the finite $q$-element field of characteristic $p$ belong to the same orbit under the natural action of the symmetric group if each of the elementary symmetric polynomials of degree…
By exploiting a symmetric scheme for coupling $N$ spin-1/2 constituents (the physical qubits) to states with total angular momentum $N/2-1$, we construct rotationally invariant logical qudits of dimension $d=N-1$. One can encode all qudit…
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
In Noncommutative Geometry, as in quantum theory, classically real variables are assumed to correspond to self-adjoint operators. We consider the relaxation of the requirement of self-adjointness to mere symmetry for operators $X_i$ which…