Nonlinear qubit transformations

Nonlinear Qubit Transformations

We generalise our previous results of universal linear manipulations [Phys. Rev. A 63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its...

Crazy Qubit Transformations

We generalise our previous results of universal linear manipulations [Phys. Rev. A 63, 032304 (2001)] to investigate three types of nonlinear qubit transformations using measurement and quantum based schemes. Firstly, nonlinear rotations are studied. We rotate different parts of a Bloch sphere in opposite directions about the z-axis. The second transformation is a map which sends a qubit to its...

On Poisson Nonlinear Transformations

We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

Certain Nonlinear Transformations

Nonlinear coordinate transformations for unconstrained optimization I. Basic transformations

In this two-part article, nonlinear coordinate transformations are discussed to simplify unconstrained global optimization problems and to test their unimodality on the basis of the analytical structure of the objective functions. If the transformed problems are quadratic in some or all the variables, then the optimum can be calculated directly, without an iterative procedure, or the number of ...