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We systematically investigate effects of partially polarized noise in a receiver. We introduce a relationship between the Q factor and the signal-to-noise ratio (SNR) that accounts for effects of partially polarized noise. We derive an expression for the distribution of the Q factor for a fixed SNR, and we validate our results by comparison to back-to-back experiments. We show that the system performance varies depending on the angle between the Stokes vectors of the signal and the noise as well as the degree-of-polarization of the noise. Highly polarized noise will cause a larger variation of the system performance.