Exact Calculations of Coherent Information for Toric Codes under Decoherence: Identifying the Fundamental Error Threshold

Understand

The toric code is a canonical example of a topological error-correcting code.

• Two logical qubits stored within the toric code are robust against local decoherence, ensuring that these qubits can be faithfully retrieved as long as the error rate remains below a certain threshold.
• Recent studies have explored such a threshold behavior as an intrinsic information-theoretic transition, independent of the decoding protocol.
• These studies have shown that information-theoretic metrics, calculated using the Renyi (replica) approximation, demonstrate sharp transitions at a specific error rate.