We use the quantum correlations of twin beams of light to investigate the fundamental addition of noise when one of the beams propagates through a fast-light medium based on phase-insensitive gain. The experiment is based on two successive four-wave mixing processes in rubidium vapor, which allow for the generation of bright two-mode-squeezed twin beams followed by a controlled advancement while maintaining the shared quantum correlations between the beams. The demonstrated effect allows the study of irreversible decoherence in a medium exhibiting anomalous dispersion, and for the first time shows the advancement of a bright nonclassical state of light. The advancement and corresponding degradation of the quantum correlations are found to be operating near the fundamental quantum limit imposed by using a phase-insensitive amplifier.