Pseudoentanglement from tensor networks

Pseudoentangled states are defined by their ability to hide their entanglement structure: they are indistinguishable from random states to any observer with polynomial resources, yet can have much less entanglement than random states. Existing constructions of pseudoentanglement based on phase- and/or subset-states are limited in the entanglement structures they can hide: e.g., the states may have low entanglement on a single cut, on all cuts at once, or on local cuts in one dimension. Here we introduce new constructions of pseudoentangled states based on (pseudo)random tensor networks that affords much more flexibility in the achievable entanglement structures. Notably these include `holographic' states whose entanglement entropy obeys a Ryu-Takayanagi minimum-cut formula, answering a question posed in [Aaronson et al., arXiv:2211.00747].