Quantum pseudorandom states are efficiently preparable states that are indistinguishable from truly Haar random states to an efficient observer. First defined by Ji, Liu and Song, such states have found a wide variety of applications in areas such as quantum gravity and cryptography. A fundamental question is exactly how much entanglement is required to create such states. Haar-random states, as well as t-designs for t ≥ 2, exhibit near maximal entanglement. Here we provide the first construction of pseudorandom states with only polylogarithmic entanglement entropy across an equipartition of the qubits, which is the minimum possible. Our construction can be based on any one-way function secure against quantum attack.

More fundamentally, our work calls into question to what extent entanglement is a "feelable" (or efficiently observable) quantity of quantum systems. Inspired by recent work of Gheorghiu and Hoban, we define a new notion which we call "pseudoentanglement", which are ensembles of efficiently constructible quantum states which hide their entanglement entropy. We show such states exist in the strongest form possible while simultaneously being pseudorandom states.

This talk is based on arXiv:2211.00747 and arXiv:2311.12017.