Did I miss one getting solved?

Please don’t leave us all in suspense!

]]>Oh, alright: the question arose a few years ago in my paper with Gottesman on stabilizer circuits (quant-ph/0406196). But there we only needed a special case (stabilizer states), which we were able to get directly.

I don’t know if the general result has any applications. Philosophically, you can think of it as a combinatorial version of Heisenberg’s uncertainty principle. Instead of saying that any state is indeterminate in either the position or momentum basis, now we’re saying that any n-qubit state is “completely indeterminate” in *some* Hadamard basis.