25 October 2022, 2pm London time - Video of talk
(University of Chicago)
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
cryptography and quantum gravity. A fundamental question is exactly
how much entanglement is required to create such states. Haar-random
states, as well as t-designs, 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. We additionally show that the entanglement in our
construction is fully "tunable".
More fundamentally, our work calls into question to what extent
entanglement is a "feelable" 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
constructable quantum states which hide their entanglement entropy. We
show such states exist in the strongest form possible while
simultaneously being pseudorandom states.
Based on joint work with Adam Bouland, Soumik Ghosh, Umesh Vazirani
and Zixin Zhou.