Robust Quantum Entanglement at (nearly) Room Temperature
Abstract
We formulate a mixed-state analog of the NLTS conjecture [FH14] by asking whether there exist topologically-ordered systems for which the thermal Gibbs state for constant temperature is globally-entangled in the sense that it cannot even be approximated by shallow quantum circuits. We then prove this conjecture holds for nearly optimal parameters: when the "inverse temperature" is almost a constant (temperature decays as 1/loglog(n))) and the Hamiltonian is nearly local (log(n)-local). The construction and proof combine quantum codes that arise from high-dimensional manifolds [Has17, LLZ19], the local-decoding approach to quantum codes [LTZ15, FGL18] and quantum locally-testable codes [AE15].
Cite
@article{arxiv.1911.04461,
title = {Robust Quantum Entanglement at (nearly) Room Temperature},
author = {Lior Eldar},
journal= {arXiv preprint arXiv:1911.04461},
year = {2020}
}
Comments
Strengthened main theorem, small modifications to the proof, revised introduction