Frobenius light cone and the shift unitary
arXiv:2402.07990 · doi:10.1103/PhysRevA.109.052419
Abstract
We bound the time necessary to implement the shift unitary on a one-dimensional ring, both using local Hamiltonians and those with power-law interactions. This time is constrained by the Frobenius light cone; hence we prove that (for certain power law exponents) shift unitaries cannot be implemented in the same amount of time needed to prepare long-range Bell pairs. We note an intriguing similarity between the proof of our results, and the hardness of preparing symmetry-protected topological states with symmetry-preserving Hamiltonians.
17 pages, 1 figure. Published version
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