Initial-state dependence of Ramsey contrast

The contrast of a phase-sensitive pulse sequence depends on the state during phase accumulation. Coherent preparation can create two populated paths whose relative quantum phase is converted to a population by readout; preparation into one path gives no such signal. For the Hadamard-phase-Hadamard qubit rotation, a pure $z$-polarized input yields full contrast, a pure $x$-polarized input yields none, and an unpolarized input also yields none. The last two cases have different purity despite identical measured populations. Purity alone is therefore not a phase-sensitivity criterion.