Optimal manipulations with qubits: Universal-NOT gate

Quantum information processing is usually associated with a specific comput ational basis. Nevertheless, for a deeper understanding of the fundamental principles of quantum computing, it is essential to investigate what is the fidelity of universal operations that are basis independent; i.e., the tas k is to perform optimally a specific operation on a qubit or a quantum regi ster that is in an unknown state. In this paper we introduce the universal- NOT gate that takes as an input a qubit in an arbitrary state \Psi] and gen erates an output that is as close as possible to the orthogonal state \Psi( perpendicular to)]. [S1050-2947(99)52110-4].