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We experimentally demonstrate polarization-insensitive all-optical clock recovery using a passively mode-locked quantum-dot Fabry-Perot (QD-FP) semiconductor laser at 40 Gb/s. Polarization insensitivity is achieved by using a wavelength conversion stage based on cross-phase modulation in a semiconductor optical amplifier and optical bandpass filtering. A clock signal with a root-mean-square timing jitter of 300 fs is recovered for an input data signal with a scrambled state-of-polarization (SOP). This is comparable to that from the QD-FP laser alone for an input signal with a fixed SOP. Moreover, an improvement in the tolerance to a degradation in the optical signal-to-noise ratio of the input signal is achieved by the use of the wavelength conversion stage.