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The whole point of an oracle-based algorithm is that it does depend on the promised structure of the oracle. For Bernstein-Vazirani, it is assumed that the oracle acts as $$ |x\rangle|y\rangle\rightarrow |x\rangle|y\oplus (x\cdot s)\rangle. $$ That is the fundamental starting point (and is just the reversible implementation of $x\cdot s$). If you didn't have ...


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Intuition is just that - intuition. It's is not an absolute of "this is how it works", but rather something that helps you get some sort of intuition about what's happening. In that sense, there is no "right" or "wrong". It's what helps you. Different people understand things in different ways. You just have to be clear that every intuitive explanation has ...


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So, this isn't a question with a single "correct" physical answer. In general, though I would say that the parallel nature of quantum algorithms is dramatically overplayed, especially in older literature and a lot of the popular science press. Remember that whatever parallelism is happening as your quantum state evolves, once you measure you're going to ...


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Finally, I found the answer myself there. The only interesting thing is the amplitude of $|0\rangle^{\oplus n}$. If the function is constant, it is $\pm 1$ and if the function is balanced, it is $0$. Hence, in the first case we are sure to measure all qubits in the $|0\rangle$ state and in the second case, we cannot measure all of them in this state (else ...


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