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arXiv · 2402.07990

Frobenius light cone and the shift unitary

Chao Yin·Andrew Lucas·David T. Stephen
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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.

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Chao Yin, Andrew Lucas, David T. Stephen. 2024-02-12. Frobenius light cone and the shift unitary. https://doi.org/10.1103/physreva.109.052419

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