Related papers: The Poincar\'e half-plane for informationally comp…
We show that a symmetric informationally-complete positive operator-valued measure exists in a given dimension $d$ if and only if there exists a $d^2$-dimensional operator system satisfying certain order-theoretic conditions. We also…
Lie algebra is a hidden mathematical structure behind various quantum systems realised in nature. Here, we consider $SU(2)$ wavefunctions for polarisation states of coherent photons emitted from a laser source, and discuss the relationship…
We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The…
We develop a comprehensive theoretical model for the interaction strength between a pair of exciton-polaritons in microcavity devices. Ab initio numerical calculations for dipolar polaritons in one dimension are used as a starting point to…
We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the…
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
We show that naturally associated to a SIC (symmetric informationally complete positive operator valued measure or SIC-POVM) in dimension d there are a number of higher dimensional structures: specifically a projector and a complex Hadamard…
A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…
This paper gives an explicit structure theorem for the symmetric group acting on the symmetric algebra of its natural module. Let $G$ be the symmetric group on $x_1,..., x_n$ and let $d_i$ be the $i^{\text{th}}$ elementary symmetric…
Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct a coarse moduli space for…
We prove an inversion theorem for recursive formulas satisfied by certain families of converging power series in two variables. These power series are indexed by the Harder-Narasimhan types of principal $G$-bundles of degree $d \in \pi_1 G$…
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce…
Mott noted a one-to-one correspondence between saturated multiplicatively closed subsets of a domain D and directed convex subgroups of the group of divisibility D. With this, we construct a functor between inclusions into saturated…
We present a new set of massless Poincar\'e group operators Hermitian with respect to the $ 1 / r $ inner product space, which have quasi-plane wave energy-momentum eigenfunctions having velocity $ c $ along their axis of propagation. These…
The finite Heisenberg group knows when the dimension of Hilbert space is a square number. Remarkably, it then admits a representation such that the entire Clifford group --- the automorphism group of the Heisenberg group --- is represented…
Given an ensemble of qubits, which we are told consists of a mixture of two pure states, one with probability $\eta_{0}$ and one with probability $\eta_{1}$, we want to find a POVM that will discriminate between the two states by measuring…
All real three dimensional Poisson-Lie groups are explicitly constructed and fully classified under group automorphisms by making use of their one-to-one correspondence with the complete classification of real three-dimensional Lie…
The Bisognano-Wichmann property on the geometric behavior of the modular group of the von Neumann algebras of local observables associated to wedge regions in Quantum Field Theory is shown to provide an intrinsic sufficient criterion for…
We give an algebraic description of several modules and algebras related to the vector partition function, and we prove that they can be realized as the equivariant K-theory of some manifolds that have a nice combinatorial description. We…
Two particles, described by an irreducible two-particle representation of the Poincar\'e group, are correlated by the constraints that the constancy of the Casimir operators imposes on the state space. This correlation can be understood as…