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Quantum error correction (QEC) is a collection of techniques to protect quantum information from decoherence and other quantum noise, to realise fault-tolerant quantum computation. Quantum error correction is expected to be essential for practical quantum computation in the face of noise on stored quantum information, faulty quantum gates, faulty state preparations, and faulty measurements. (Wikipedia)
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Error correction conditions for bit flip code
I am reading Nielsen and Chuang's chapter on error correction. I have a very basic question about this theorem:
Theorem 10.8 (Error-correction conditions for stabilizer codes):
Let $S$ be the stabiliz …