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2

First, give an illustration of a linear system. You know you have to eat healthy, so you are prepared to pay 50 cents for an apple. But the next day, if apple prices double, you will forget the health benefits. Now a non linear system, because it's based on people's reaction to supply and demand. An everyday example based on the Uber taxis system. Uber ...


3

Wrote this to address the 2nd question in the OP: "Is it possible to derive a generalized HUP from a nonlinear modification of quantum theory (Invent some nonlinear observables that is neither position nor momentum)?", following the discussion on the topic in comments. Although it is not a clear-cut answer, perhaps it may help. But first a couple of ...


4

Aaronson's claims are true, but your statement about what he means is not correct. If cloning were possible, the HUP would still exist but would pose a non-absolute limit on how much you could learn about a single copy of an unknown quantum state- that is, any limit on how much you learned about a state could be attributed to not doing a very good ...


6

If you go through the proof of the no-cloning theorem (see e.g. wikipedia) you will notice that only the following properties are used: Unitarity of the evolution operator Hilbert space axioms for a composite state $|\phi \rangle | 0 \rangle$ (which imply the Cauchy-Schwartz inequality) The no-cloning theorem than says that no unitary operator exists ...



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