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Feb 25, 2023 at 22:14 comment added benrg @tparker I'm using the convention that "copies" of $α|0\rangle+β|1\rangle$ are $α|0\rangle^a+β|1\rangle^a$ and "clones" are $(α|0\rangle+β|1\rangle)^a$, with the name of the no-cloning theorem as my justification. I could change the language, but I don't want to complicate it too much, especially when the Dirac notation resolves the ambiguity anyway.
Feb 25, 2023 at 15:53 comment added tparker Minor nitpick: the state $\sqrt{\frac{2}{3}} |0^a\rangle + \sqrt{\frac{1}{3}} |1^a\rangle$ is not "$a$ copies of the original qubit" $\sqrt{\frac{2}{3}} |0\rangle + \sqrt{\frac{1}{3}} |1\rangle$. That would be $\left( \sqrt{\frac{2}{3}} |0\rangle + \sqrt{\frac{1}{3}} |1\rangle \right)^{\otimes a}$, which contains lots of cross terms.
May 11, 2022 at 19:43 comment added benrg @Sandejo I omitted certain things from the state vectors I wrote down, which in this experiment includes Alice's memory of the initial preparation. I agree it's confusing and I'll think about rewriting it.
May 10, 2022 at 19:11 comment added Sandejo In your simpler experiment, why should Alice be surprised to measure $1$ when the lab is in the state $\lvert1^a\rangle$? In this state, wouldn't it be the case that Alice prepared the system in the state $\lvert1\rangle$?
May 7, 2022 at 1:47 comment added benrg @The_Sympathizer Oh, of course Scott Aaronson decoded the paper before me. I don't know why I didn't check his blog. The post title is a perfect summary, too. He doesn't go nearly as far as me in tearing it apart, though. He doesn't seem to think it was wrong to publish it in this form (comment #6), which I do, because there seem to be outright errors that were missed by the reviewers – particularly that the argument separately violates each named assumption in various ways, unless I missed something.
May 7, 2022 at 0:53 comment added The_Sympathizer I came to pretty much the exact same conclusion at the end, as did Scott Aaronson: scottaaronson.blog/?p=3975. The real trick is in those crooked-basis measurements.
May 6, 2022 at 23:27 comment added knzhou This is the clearest explanation of that paper I've ever seen, I hope this gets the attention it deserves!
May 6, 2022 at 23:23 history answered benrg CC BY-SA 4.0