
Two possible quantum descriptions of the classical NOT
gate are investigated in the framework of the Hilbert space C2: the unitary
and the antiunitary operator realizations. The two cases are distinguished
interpreting the unitary NOT as a quantum realization of the classical
gate which on a fixed orthogonal pair of unit vectors, realizing once
for all the classical bits 0 and 1, produces the required transformations
from 0 to 1 and from 1 to 0 (i.e., logical quantum NOT). The antiunitary
NOT is a quantum realization of a gate which acts as a classical NOT on
any pair of mutually orthogonal vectors, each of which is a potential
realization of the classical bits (i.e., universal quantum NOT).
