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5

All tensor products of $n$ Pauli operators $\{I,X,Y,Z\}$ (that is $4^n$ combinations) form an orthogonal basis for the vector space of $2^n \times 2^n$ complex matrices. Hence, for every matrix there is a unique decomposition as a linear combination of tensor products of Pauli unitaries. Same is true if we fix some other unitary basis. If we not fix the ...


2

First of all, are the ancilla qubits entangled with $|\psi\rangle$? Yes, depending on what the state is. Let's say you started with $$ \alpha|000\rangle+\beta|111\rangle, $$ but it has experienced an error of $(\cos\theta I+i\sin\theta X)$ on the first qubit. So, your state becomes $$ \cos\theta(\alpha|000\rangle+\beta|111\rangle)+i\sin\theta(\alpha|100\...


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