Related papers: From SICs and MUBs to Eddington

In this work, we stress the existence of isomorphisms which map complex contours from the upper half to contours in the lower half of the complex plane. The metric operator is found to depend on the chosen contour but the maps connecting…

Constructing four six-dimensional mutually unbiased bases (MUBs) is an open problem in quantum physics and measurement. We investigate the existence of four MUBs including the identity, and a complex Hadamard matrix (CHM) of Schmidt rank…

We introduce one of the most beautiful algebraic varieties known, a quintic hypersurface in projective five-space, which is invariant under the action of the Weyl group of $E_6$. This variety is intricately related with many other moduli…

In this study, we define a brief description of the hyperbolic and elliptic rotational surfaces using a curve and matrices in 4-dimensional semi Euclidean space. That is, we provide different types of rotational matrices, which are the…

The Hessian of a general cubic surface is a nodal quartic surface, hence its desingularisation is a K3 surface. We determine the transcendental lattice of the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt points…

Let $X$ be a compact connected Riemann surface and $D$ an effective divisor on $X$. Let ${\mathcal N}_H(r,d)$ denote the moduli space of $D$-twisted stable Higgs bundles (a special class of Hitchin pairs) on $X$ of rank $r$ and degree $d$.…

Mutually unbiased bases (MUB) have many applications in quantum information processing and quantum cryptography. Several complex MUB's in $\mathbb{C}^d$ for some dimension $d$ and with larger size have been constructed. On the other hand,…

We study SU(4)-symmetric Heisenberg model on the cubic lattice with spatially anisotropic magnetic couplings. We utilize several approaches based on the tensor-network representation of the many-body wave functions, which enable accurate…

We discuss some applications of higher symmetry groups to condensed matter systems. We give special attention to the groups SO(n) (n = 4, 5, 6, 8) in the two-dimensional Hubbard model and its generalizations, which model the high T_c…

We define symmetry classes and commutation symmetries in the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites and investigate them by means of tools from the representation theory of symmetric groups S_N such as…

We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM),…

Analysis of state reconstruction both classical and quantum mechanical on equal footing is outlined. The meaning of "mutual unbiased bases" (MUB) of Hilbert spaces is explained in detail. An alternative quantum state reconstruction, that…

We consider generalisations of the elliptic Calogero--Moser systems associated to complex crystallographic groups in accordance to [1]. In our previous work [2], we proposed these systems as candidates for Seiberg--Witten integrable systems…

We establish a connection between the problem of constructing maximal collections of mutually unbiased bases (MUBs) and an open problem in the theory of Lie algebras. More precisely, we show that a collection of m MUBs in K^n gives rise to…

Recently, Zhu classified all the SIC-POVMs whose symmetry groups act doubly transitively. Lattices of integers in the complex numbers, the quaternions and the octonions yield the key parts of these symmetry groups.

In this work, the concept of mutually unbiased frames is introduced as the most general notion of unbiasedness for sets composed by linearly independent and normalized vectors. It encompasses the already existing notions of unbiasedness for…

We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semi-simple Lie algebra and finite order automorphisms. For example, the non-linear Schr\"odinger…

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths…

The closed 3-manifolds of constant positive curvature were classified long ago by Seifert and Threlfall. Using well-known information about the orthogonal group O(4), we calculate their full isometry groups Isom(M), determine which elliptic…