In this paper, we consider the class of linear space time block codes (STBCs) that possess the following properties: i) enabling full antenna diversity, ii) preserving the modulus of information symbols, and iii) achieving the maximum rate of one symbol per channel use under i) and ii). We first provide an alternative construction for full-diversity rate-one STBCs that are based on linear const...

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

Similarly to quantum states, operations can also be transformed by means of superchannels, known as process matrices. Quantum superchannels with multiple slots are deterministic transformations which take independent inputs. While they enforced respect the laws mechanics, use input may lack a definite causal order, and characterizations general in terms objects physical implementation have been...

In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach chosen goal subspace. The questions studied in are motivated by recent results dynamics graphs, most particularly Markov chains. We focus describing how and times can be obtained, main novelties res...

If an open quantum system is initially uncorrelated from its environment, then dynamics can be written in terms of a Lindblad-form master equation. The equation divided into unitary piece, represented by effective Hamiltonian, and dissipative hermiticity-preserving superoperator; however, the division pieces non-unique. For finite-dimensional systems, we resolve this non-uniqueness specifying n...

Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category. Unitary R-matrices, namely unitary solutions to the Yang-Baxter equation, afford explicitly local unitary representations of braid groups. Inspired by topological quantum computation, we study whether or not it is...