 Quantum coherence in a specified basis

For a chosen orthonormal basis, the off-diagonal entries of a density operator encode quantum coherence between distinct basis states. A diagonal density operator is an incoherent mixture in that basis. This property is basis-dependent: diagonalizing the operator does not imply that it lacked coherence in the measurement or energy basis of interest. Relative phases affect these entries, while a global wavefunction phase cancels from the density operator. Dephasing damps the entries and can spoil stimulated Raman adiabatic passage by removing the ground-state interference that maintains the dark state.