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arXiv · 2204.00908

Complexity and entanglement in non-local computation and holography

Alex May
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Abstract

Does gravity constrain computation? We study this question using the AdS/CFT correspondence, where computation in the presence of gravity can be related to non-gravitational physics in the boundary theory. In AdS/CFT, computations which happen locally in the bulk are implemented in a particular non-local form in the boundary, which in general requires distributed entanglement. In more detail, we recall that for a large class of bulk subregions the area of a surface called the ridge is equal to the mutual information available in the boundary to perform the computation non-locally. We then argue the complexity of the local operation controls the amount of entanglement needed to implement it non-locally, and in particular complexity and entanglement cost are related by a polynomial. If this relationship holds, gravity constrains the complexity of operations within these regions to be polynomial in the area of the ridge.

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Alex May. 2022-04-02. Complexity and entanglement in non-local computation and holography. https://doi.org/10.22331/q-2022-11-28-864

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