  We demonstrate that reversible dephasing via inhomogeneous broadening can
greatly reduce collective quantum state rotation errors, and observe the
suppression of rotation errors by more than 21 dB in the context of collective
population measurements of the spin states of an ensemble of $2.1 \times 10^5$
laser cooled and trapped $^{87}$Rb atoms. The large reduction in rotation noise
enables direct resolution of spin state populations 13(1) dB below the
fundamental quantum projection noise limit. Further, the spin state measurement
projects the system into an entangled state with 9.5(5) dB of directly observed
spectroscopic enhancement (squeezing) relative to the standard quantum limit,
whereas no enhancement would have been obtained without the suppression of
rotation errors.
