Nonlinear qubit transformations - art. no. 032301

We generalize our previous results of universal linear manipulations [Phys. Rev. A 63, 032304 (2001)] to investigate three types of nonlinear qubit tr ansformations using measurement and quantum-based schemes. First. nonlinear rotations are studied. We rotate different parts of a Bloch sphere in oppo site directions about the z axis. The second transformation is a map that s ends a qubit to its orthogonal state. We consider the case in which the ort hogonal state is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e., (theta,phi)-->(theta-alpha,ph i), again applied only to part of the Bloch sphere. In order to achieve the se three operations, we consider different measurement preparations and der ive the optimal average (instead of universal) quantum unitary transformati ons. We also introduce a simple method for a qubit measurement and its appl ication to other cases.