Quantum Error Correction in SYK and Bulk Emergence

Understand

We analyze the error correcting properties of the Sachdev-Ye-Kitaev model, with errors that correspond to erasures of subsets of fermions.

• We study the limit where the number of fermions erased is large but small compared to the total number of fermions.
• We compute the price of the quantum error correcting code, defined as the number of physical qubits needed to reconstruct whether a given operator has been acted upon the thermal state or not.
• By thinking about reconstruction via quantum teleportation, we argue for a bound that relates the price to the ordinary operator size in systems that display so-called detailed size winding of Nezami et al.