We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark’s theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to find an implementation of a given group-covariant POVM by a quantum circuit using its symmetry. Based on representation theory of the symmetry group we deve...

In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and WeylHeisenberg group on the two-torus are constructed. This analysis extends the well known situation for the noncommutative torus based on the algebra of the noncommuting position operators only. When considering t...

A candidate action for an Exceptional E8 gauge theory of gravity in 8D is constructed. It is obtained by recasting the E8 group as the semi-direct product of GL(8, R) with a deformed Weyl-Heisenberg group associated with canonical-conjugate pairs of vectorial and antisymmetric tensorial generators of rank two and three. Other actions are proposed, like the quartic E8 group-invariant action in 8...

Do co-adjoint orbits of Lie groups support a Kähler structure? We study this question from point view derived coherent states. examine three examples groups: the Weyl–Heisenberg group, SU(2) and SU(1, 1). In cases, where admit structure, we show that states give us embedding orbit into projective Hilbert space. contrast, squeezed (which like states, also saturate uncertainty bound) only symplec...