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However, here it is important to note that the exponentially large value of IPR ζ does not automatically imply that the eigenstates are chaotic. Indeed, following Shor [5], one can imagine a perturbation which rotates each qubit from a state |00...0 > on a random angle. In this way exponentially many quantum register states |ψ, > are present in one new eigenstate and exponentially many of them are excited after a finite time of rotation. Nevertheless, these states are not complex/chaotic and the level statistics P(s) remains poissonian with n = 1. 50. Flambaum, V. V., quant-ph/9911061.
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