  Entanglement is a quantum resource, in some ways analogous to randomness in
classical computation. Inspired by recent work of Gheorghiu and Hoban, we
define the notion of "pseudoentanglement'', a property exhibited by ensembles
of efficiently constructible quantum states which are indistinguishable from
quantum states with maximal entanglement. Our construction relies on the notion
of quantum pseudorandom states -- first defined by Ji, Liu and Song -- which
are efficiently constructible states indistinguishable from (maximally
entangled) Haar-random states. Specifically, we give a construction of
pseudoentangled states with entanglement entropy arbitrarily close to $\log n$
across every cut, a tight bound providing an exponential separation between
computational vs information theoretic quantum pseudorandomness. We discuss
applications of this result to Matrix Product State testing, entanglement
distillation, and the complexity of the AdS/CFT correspondence. As compared
with a previous version of this manuscript (arXiv:2211.00747v1) this version
introduces a new pseudorandom state construction, has a simpler proof of
correctness, and achieves a technically stronger result of low entanglement
across all cuts simultaneously.
