the Dense-Sparse Learning Parity

Pseudoentanglement in constant depth: How trivial states can have non-trivial entanglement structure

arXiv:2605.31448v1 Announce Type: cross Abstract: We construct a family of 2D-local constant-depth quantum circuits that output states whose entanglement entropy across a specified cut cannot be estimated in quantum polynomial time. As constant-depth quantum circuits can be learned from polynomially many quantum samples, our resulting pseudoentangled states are implicitly public-key and not pseudorandom. This separates pseudoentanglement from pseudorandomness in the shallow-circuit regime:...