We discuss the differing definitions of complex and quaternionic projective group representations employed by us and by Emch. The definition of Emch (termed here a strong projective representation) is too restrictive to accommodate quaternionic Hilbert space embeddings of complex projective representations. Our definition (termed here a weak projective representation) encompasses such embedding...

Using the centro-symmetry property of uniform linear array (ULA), we propose an algorithm that combines the weighted l2;1 minimization with the unitary transformation to improve the performance of DOA estimation. Exploiting the result of the unitary transformation, more credible weights can be obtained and the jointly sparse constraint can be further enhanced. Moreover, the unitary transformati...

We introduce and discuss the properties of a new class of finite-dimensional frames with strong symmetry properties called geometrically uniform (GU) frames, that are defined over a finite abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by a finite abelian group of unitary...

According to a fundamental result in quantum computing, any unitary transformation on composite system can be generated using so-called 2-local unitaries that act only two subsystems. Beyond its importance this also regarded as statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints short-term dynamics, it does not restrict possible evolutions...

The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.

We report the study of spontaneous magnetization (i.e., spin-polarization) for time-reversal symmetry (TRS)-breaking superconductors with unitary pairing potentials, in absence external magnetic fields or Zeeman fields. Spin-singlet ($\Delta_s$) and spin-triplet ($\Delta_t$) pairings can coexist whose crystal structure lacks inversion symmetry. The TRS be spontaneously broken once a relative ph...

Classification of states of quantum channels of information transfer is built on the basis of unreducible representations of qubit state space group of symmetry and properties of density matrix spectrum. It is shown that pure disentangled states form two-dimensional surface, and the reason of state disentanglement is in degeneration of non-zero density matrix eigenvalues. 1 Group of symmetry of...

A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford a...