We analyze the color performance and system efficiency of three commonly employed liquid crystal display modes with a blue LED-pumped red and green quantum dots (QDs) backlight. Based on the measured QD emission spectra, we can achieve 115% color gamut in CIE 1931 and 140% in CIE 1976 color space, while keeping the same energy efficiency as conventional backlights. Next, we apply multi-objective optimization method to refine the QD emission spectra and find a fundamental tradeoff between display system efficiency and color gamut. This systematic photometric analysis also provides useful guidelines for further optimizing QD backlight design and display system efficiency.