A dephasing channel suppresses off-diagonal entries of a density matrix in a preferred basis while preserving quantum state populations. Complete dephasing is identical to a projective measurement in that basis with its outcome discarded.
For the Bell correlations versus a classical mixture example, completely dephasing Alice's qubit in the computational basis maps to . It preserves their perfect agreement and each reduced density matrix, yet destroys the correlation. This is why testing only populations can miss damage to a quantum memory: the stored quantum coherence may have disappeared while every preferred-basis measurement still looks correct. The joint Von Neumann entropy rises from zero to one bit, although each local entropy stays fixed.
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