We provide a physical prescription based on interferometry for introducing the total phase of a mixed state undergoing unitary evolution, which has been an elusive concept in the past. We define the parallel transport condition that provides a connection form for obtaining the geometric phase for mixed states. The expression for the geometric phase for mixed state reduces to well known formulas...

Abstruef-This paper addresses the design of a novel scheme that combines error control coding (EC) and unitary precoding (UP) in order to obtain high diversity gains in OFDM systems with low complexity. The overall diversity of the proposed system is shown to be the product of the individual diversities achievable by the error control coding and by the unitary precoding, while the complexity is...

We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equiva...

On one-dimensional two-way infinite lattice system, a property of stationary (space-) translationally invariant states with nonvanishing current expectations are investigated. We consider GNS representation with respect to such a state, on which we have a group of space-time translation unitary operators. We show, by applying Goldstone-theoremlike argument, that spectrum of the unitary operator...

We introduce a simple uniform structure of elementary Φ-unitary matrices. Elementary Φ-unitary transformations are the extentions of Householder transformations in real and complex spaces with a definite or an indefinite inner product induced by a nonsingular signature matrix Φ. The extentions are found useful in the computations of complex matrices or special structured matrices. For two (comp...

In this paper, we consider the amplified-and-forward relaying in an OFDM system with unitary linear processing at the relay. We proposed a general analytical framework to find the unitary linear processing matrix that maximizes the system achievable rate. We show that the optimal processing matrix is a permutation matrix, which implies that a subcarrier pairing strategy is optimal. We further d...