Understanding Qubits and Complex Scalars: The Role of Imaginary Numbers

[kaje]

Hi,

Does anybody know why we have complex scalers to represent qubits..I mean why they are not real numbers.

Thanks

 

[Strilanc]

What does it matter that they're not real numbers? There are complex numbers that don't correspond to the number of cows you can have in a field... so what? You also can't have -1 cows in a field, or fit fifty trillion cows in a field. While we're at it, you can't have "F=ma" cows in a field either.

We're not counting cows in fields, so why would we expect to only use mathematical abstractions matched to that task?

I really just don't see the problem here. We have a mathematical model that works, we know how to map between the model and reality, and the model happens to internally use values that are good at representing 2d positions, translations, and rotations. There's nothing amiss. We can rewrite our laws to use pairs of real numbers instead of complex numbers, but why would we do that? It would just double the amount of symbol manipulation.

 

[bhobba]

See the following thread:
https://www.physicsforums.com/threads/complex-numbers-and-physical-meaning.839613/

Thanks
Bill

 

[bhobba]

I really just don't see the problem here. We have a mathematical model that works, we know how to map between the model and reality, and the model happens to internally use values that are good at representing 2d positions, translations, and rotations. There's nothing amiss. We can rewrite our laws to use pairs of real numbers instead of complex numbers, but why would we do that? It would just double the amount of symbol manipulation.

That's true.

I interpret such questions as why do we have complex numbers in QM for which there are quite a few reasons.

Thanks
Bill