Abstract
We find the optimal universal way of manipulating a single qubit, such that Such optimal transformations fall into two classes. For the optimal map is the identity and the fidelity varies monotonically from 1 (for to (for For the optimal map is the universal-NOT gate and the fidelity varies monotonically from (for to (for The fidelity is equal to the fidelity of measurement. It is therefore rather surprising that for some values of the fidelity is lower than For instance, a universal square root of NOT operation is more difficult to approximate than the universal NOT gate itself.
- Received 8 August 2000
DOI:https://doi.org/10.1103/PhysRevA.63.032304
©2001 American Physical Society