Pseudoentanglement in constant depth: How trivial states can have non-trivial entanglement structure
The paper explores 'pseudoentanglement,' where states from shallow quantum circuits possess entanglement structures that are hard to estimate, unlike standard pseudorandom states. It shows that publicly prepared circuits can yield states with an additive entanglement entropy gap, proving a separation between pseudoentanglement and pseudorandomness in the constant-depth regime.