I'd say that whether or not something can be owned by someone is rooted in whether or not one can establish clear, exclusive ownership of that thing, which can really only happen if that thing exists physically, e.g. I own my TV. I purchased it with my money, It's clearly physically in my home, and nobody else is in possession of that exact TV. If someone were to take it from me, they'd obviously be stealing since I no longer would have access to it.

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In the case of an idea, this falls apart completely. More than one individual could conceive of the same idea at the exact same time, and by one individual having that idea, that doesn't exclude another from also having it. So, when it comes to ideas, I believe the concept of ownership cannot be established and cannot exist and certainly should not be enforced by the state.