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>The tensor product itself captures all ways that basic things can 'interact' with each other! In quantum physics, "interacting" usually has a different meanin
by sigmoid10 3y ago
>The tensor product itself captures all ways that basic things can 'interact' with each other!
In quantum physics, "interacting" usually has a different meaning. So one should use these terms more carefully.
>And you need the tensor product already for pure states in QM.
No. Pure states are just vectors (or more precise: rays) in Hilbert space. The usual inner product is sufficient to work with them. An outer (=tensor) product of these states will just give you a density matrix with tr(ρ^2)=1.
- hackandthink 3y ago"Product states are multipartite quantum states that can be written as a tensor product" "In the special case of pure states the definition simplifies: a pure state is separable if and only if it is a product state." https://en.wikipedia.org/wiki/Separable_state https://en.wikipedia.org/wiki/Separable_state
- sigmoid10 3y agoKeyword is can. There's a reason why most university level physics curricula defer quantum density matrices (and by extension tensor algebra) to more advanced classes. There's a lot of mathematical legwork required before you can actually make use of that.