Quantum error correction (QEC) is the set of techniques used to protect fragile quantum information from noise, decoherence, and imperfect control. Unlike classical error correction, QEC cannot simply copy a qubit’s state to check it later, because measuring a quantum state generally destroys the superposition that carries the information — the no-cloning theorem forbids copying it directly.
Instead, QEC codes spread one “logical” qubit’s information redundantly across many physical qubits, and use indirect syndrome measurements to detect and correct errors without learning the encoded state itself. How much physical-qubit overhead a given code requires, and how quickly that overhead shrinks as hardware improves, are central questions on the path to large-scale, fault-tolerant quantum computers.
A standard way to quantify how well a code (or more generally, a noisy channel) preserves quantum information is the coherent information , the difference of von Neumann entropies of a reference system’s output after part of an entangled state passes through the channel. A coherent information that stays close to its maximum after erasing part of the code means the erased information is recoverable; how quickly it degrades as the erased region grows is a common way to compare the robustness of different code constructions.