# Fun with replicas: tripartitions in tensor networks and gravity

@inproceedings{Penington2022FunWR, title={Fun with replicas: tripartitions in tensor networks and gravity}, author={Geoffrey Penington and Michael Walter and Freek Witteveen}, year={2022} }

: We analyse a simple correlation measure for tripartite pure states that we call G ( A : B : C ) . The quantity is symmetric with respect to the subsystems A , B , C , invariant under local unitaries, and is bounded from above by log d A d B . For random tensor network states, we prove that G ( A : B : C ) is equal to the size of the minimal tripartition of the tensor network, i.e., the logarithmic bond dimension of the smallest cut that partitions the network into three components with A , B…

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