= Decoherence-free subspace
{wiki=Decoherence-free_subspaces}
A subspace on which every operator in a specified noise model acts as a common scalar, so the encoded <density operator> is preserved without syndrome-dependent recovery. For collective $z$ rotations, the span of $|01\rangle$ and $|10\rangle$ has zero total $Z$ eigenvalue and is invariant. Protection depends on the collective-noise assumption; independent local rotations do not generally preserve its logical phase.
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