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In quantum error correction literature, it is assumed that the possibility of happening a few-qubit error is bigger than a many-qubit error. Does this assumption have any physical evidence? I am looking for relevant references.

For example, in the Shor's 9-qubit code \begin{aligned} & |\overline{0}\rangle=(|000\rangle+|111\rangle)(|000\rangle+|111\rangle)(|000\rangle+|111\rangle) \\ & |\overline{1}\rangle=(|000\rangle-|111\rangle)(|000\rangle-|111\rangle)(|000\rangle-|111\rangle) \end{aligned} What physical mechanism makes that $X_1$ error happen more frequently rather than $X_1\otimes X_2$ error?

This question of course has a classical version. For example, in the classical repetition code, it is assumed that each bit will flip independently with some certain probability since the registers storing two different bits are not interacting with each other. But in the quantum case, the qubits can be entangled together, so I cannot believe this independence assumption is obvious.

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