> well, in that sense the op was saying disregard the real factors of complex numbers, use only 1 and i.
This is incorrect. The quantum mechanics of discrete systems still requires the use of the continuous field of complex numbers for the amplitudes of different configurations (not just the fourth roots of unity or anything like that). The "discrete" refers to the discreteness of the configuration space (e.g., the discrete spin of an electron, in contrast to the continuous position x of a particle).
Very analogously, one can do classical probability theory for discrete (e.g., binary) outcomes or continuous ones, but either way you need to use the continuous interval between 0 and 1 to represent probabilities for those outcomes. Restricting to binary probabilities (i.e., true or false) would be classical logic, a subset of probability theory.
(It's possible to work with an equivalent formulation of quantum mechanics with only real numbers, rather than complex amplitudes, but these numbers must still be continuous and allowed to go negative. The Wigner representation is an example.)
Incidentally, mixing up the continuity of the amplitude with the continuity of configurations is exactly the sort of mistake it's easy to make when these things are introduced simultaneously! So your misconception is exceedingly reasonable.
This is incorrect. The quantum mechanics of discrete systems still requires the use of the continuous field of complex numbers for the amplitudes of different configurations (not just the fourth roots of unity or anything like that). The "discrete" refers to the discreteness of the configuration space (e.g., the discrete spin of an electron, in contrast to the continuous position x of a particle).
Very analogously, one can do classical probability theory for discrete (e.g., binary) outcomes or continuous ones, but either way you need to use the continuous interval between 0 and 1 to represent probabilities for those outcomes. Restricting to binary probabilities (i.e., true or false) would be classical logic, a subset of probability theory.
(It's possible to work with an equivalent formulation of quantum mechanics with only real numbers, rather than complex amplitudes, but these numbers must still be continuous and allowed to go negative. The Wigner representation is an example.)
Incidentally, mixing up the continuity of the amplitude with the continuity of configurations is exactly the sort of mistake it's easy to make when these things are introduced simultaneously! So your misconception is exceedingly reasonable.