Nonlinear Qubit Transformations

Preprint

17 June 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.quant-ph/0102100

Abstract

We generalise our previous results of universal linear manipulations [Phys. Rev. A63, 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 orthogonal state (which we define as ORTHOG). We consider the case when the ORTHOG is applied to only a partial area of a Bloch sphere. We also study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi), again, applied only to part of the Bloch sphere. In order to achieve these three operations, we consider different measurement preparations and derive the optimal average (instead of universal) quantum unitary transformations. We also introduce a simple method for a qubit measurement and its application to other cases.

Keywords

All Related Versions

Version 1, 2001-02-20, ArXiv
Version 2, 2001-06-17, ArXiv
Published version: Physical Review A, 64 (3), 032301.

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