Non-linear quantum state transformation of

A non-linear quantum state transformation is presented. The transformation, which operates on pairs of spin- 1 2 , can be used to distinguish optimally between two non-orthogonal states. Similar transformations applied locally on each component of an entangled pair of spin- 1 2 can be used to transform a mixed non-local state into a quasi-pure maximally entangled singlet state. In both cases the transformation makes use of the basic building block of the quantum computer, namely the quantum-XOR gate.