in this work, using eigenvalues and eigenvectors of unitary cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing pst occurring in its unitary cayley graph. moreover, we have some developments when $r$ is a product of local rings.

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

A special class of quantum channels, named subspace local (SL), are defined and investigated. The proposed definition of subspace locality of quantum channels is an attempt to answer the question of what kind of restriction should be put on a channel, if it is to act ‘locally’ with respect to two ‘locations’, when these naturally correspond to a separation of the total Hilbert space in an ortho...

0. Introduction. Throughout this paper T will denote a measure preserving transformation on a cr-finite infinite measure space (X, (B, m) which is point isomorphic with the Lebesgue measure space of the real line. Unless otherwise stated, T will be one-one. Equations involving functions or sets will always be interpreted modulo sets of measure zero. T is said to be ergodic if T~1E = E, ££(B, im...

The isomorphisms between projective unitary congruence groups are known when the underlying Witt indices are 33, the underlying spaces are finite dimensional, and the underlying integral domains are commutative [15, 161. Here we extend these results to noncommutative domains possessing a division ring of quotients and to arbitrary dimensions. Our development allows unitary and symplectic groups...

Abstract Unitary dynamics with a strict causal cone (or “light cone”) have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension completely classified by an index theory. Physical systems often exhibit only approximate cones; Hamiltonian evolutions on lattice satisfy Lieb–Robinson bounds rather than locality. This motivates us to stud...

This letter proposes a new practical multiuser MIMO (MU-MIMO) scheme, which is an evolution of the well-known Per User Unitary beamforming Rate Control (PU2RC) proposed for 3GPP-LTE and IEEE802.16m standards. The proposed scheme includes an efficient user scheduling algorithm which alleviates the major weakness of the conventional PU2RC. Numerical results show that the proposed scheme provides ...

We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family channels given by completely positive (CP) maps $M_3({\bf C}) \mapsto M_3({\bf C})$ which are both trace-preserving. Almost every member this is factorizable extreme in the set CP trace-preserving, but not either or trace-preserving maps. also large generalize Werner-Holevo channel ...

in this paper, we give a characterization of strongly jordan zero-product preserving maps on normed algebras as a generalization of  jordan zero-product preserving maps. in this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly jordan zero-product preserving maps are completely different. also, we prove that the direct p...

The two-qubit canonical decomposition SU(4) = [SU(2)⊗ SU(2)]∆[SU(2)⊗ SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2n) = KAK. The group K fixes a bilinear form related to the co...