Bounds on semi-device-independent quantum random-number expansion capabilities

The randomness expansion capabilities of semi-device-independent (SDI) prepare and measure protocols are analyzed under the sole assumption that Hilbert state dimension is known. It explicitly proved maximum certifiable entropy can be obtained through this set $\ensuremath{-}{log}_{2}[\frac{1}{2}(1+\frac{1}{\sqrt{3}})]$ same independent witnesses used to certify protocol. minimum number preparation measurement settings required achieve also proven. An SDI protocol generates output with least amount input setting provided. analytical relationship between generated witness value obtained. established as soon crosses classical bound, making noise-robust useful in practical applications.