Pseudoentanglement
0Soumik Ghosh (University of Chicago)
https://simons.berkeley.edu/talks/soumik-ghosh-university-chicago-2024-03-22
Quantum Complexity: Quantum PCP; Area Laws; and Quantum Gravity
In this talk we will discuss 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. Consequently, we prove that there is no efficient algorithm for measuring the entanglement of an unknown quantum state, under standard cryptographic assumptions. We will talk about applications of this construction to diverse areas such as property testing and holography. We will then discuss recent constructions of so-called "public key" pseudoentanglement, which are pseudoentangled quantum states that remain secure even if we give the adversary access to a quantum circuit that prepares these states. As a corollary we prove the existence of local Hamiltonians whose ground states are pseudoentangled.
Based on arXiv:2211.00747 and arXiv:2311.12017.