Local Hamiltonians with Approximation-Robust Entanglement

Understand

Quantum entanglement is considered, by and large, to be a very delicate and non-robust phenomenon that is very hard to maintain in the presence of noise, or non-zero temperatures.

• In recent years however, and motivated, in part, by a quest for a quantum analog of the PCP theorem researches have tried to establish whether or not we can preserve quantum entanglement at "constant" temperatures that are independent of system size.
• This would imply that any quantum state with energy at most, say 0.05 of the total available energy of the Hamiltonian, would be highly-entangled.
• To this date, no such systems were found, and moreover, it became evident that even embedding local Hamiltonians on robust, albeit "non-physical" topologies, namely expanders, does not guarantee entanglement robustness.