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Hi Nathan; Thanks for the catch on the occasional misuse of the phrase “Tsirelson Bound”… That’s an easy fix, at least!
On the more substantive issues, I do think that it will turn out that symmetry will play the main no-signaling role for even partially entangled states. You’re right that some of the symmetries will disappear in those cases, but some of the no-signaling disappears as well, in a certain sense. Namely, for maximally entangled states, there’s not even *self-signaling*; Alice can’t even signal to her own output, let alone Bob’s output. (Thanks to Pete Evans for bringing this to my attention.) Once the maximal-symmetry is broken, by going to partially-entangled states, self-signaling reappears (although of course Alice-Bob signaling does not). I can’t quite prove that the remaining no-signaling is due to a symmetry, since I don’t have the partially-entangled model working quite yet, but stay tuned…
You’re absolutely right about the entropy issue being connected with not being able to signal to the past, of course. Take a look at section 4 of a piece I wrote with Huw Price, which is essentially the same argument you make above. (So maybe these models are “good” in the sense you mention after all.)
That said, I still haven’t properly sorted out the objective and subjective roles of entropy on signaling… Some of the signaling asymmetry is certainly due to the effect of entropy on consciousness (we don’t know the future), and some is due to the direct accessiblity of low-entropy sources by experimenters. Right now I’m leaning towards putting most of the explanatory burden on the subjective (consciousness) side, and very little on the objective (source) side, but I need to set aside some time to think about all this more carefully and systematically. Your post has motivated me to do just that! 🙂
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