Given two arbitrary states, $|\psi\rangle\ \text{and}\ |\phi\rangle$ that are possibly unknown to the preparer, is there a way to prepare the superposition $|\psi\rangle+|\phi\rangle$ of them? (If it's generally impossible, would demanding orthogonality between them help?)
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No, you can't do it. See https://arxiv.org/abs/1505.04955 Orthogonality by itself doesn't help either.
DaftWullie
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