The physical implementation of the quantum Control-Not gate for a two-spin system is investigated numerically. The concept of a generalized quantum Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a resonant π-pulse provides a simple example of a generalized quantum Control-Not gate.

The structure of a sofic shift space is investigated, and Krieger’s embedding theorem and Boyle’s factor theorem are generalized to a large class of sofic shifts.

Given matrices A and B shift equivalent over a dense subring R of R, with A primitive, we show that B is strong shift equivalent over R to a primitive matrix. This result shows that the weak form of the Generalized Spectral Conjecture for primitive matrices implies the strong form. The foundation of this work is the recent result that for any ring R, the group NK1(R) of algebraic K-theory class...

Color digital holography (DH) has been researched in various fields such as the holographic camera and microscope because it acquires a realistic color object wave by measuring both amplitude phase. Among methods for DH, phase-shifting DH an advantage of obtaining signal objects without autocorrelation conjugate noises. However, this method usually requires many interferograms to obtain signals...