What is the role of entanglement in quantum error correction, and how do entangled states enable fault-tolerant quantum computation?

Entanglement plays a crucial role in quantum error correction by enabling the encoding of quantum information into entangled states that can detect and correct errors. Quantum error-correcting codes, such as the Shor code and surface codes, use entanglement to distribute information across multiple qubits, allowing for the identification and correction of errors without measuring the quantum state directly. This redundancy and the use of entanglement ensure that quantum computations can be performed fault-tolerantly, maintaining coherence despite the presence of errors.