  Ability to read-out the state of a single confined spin lies at the heart of
solid-state quantum information processing. While all-optical spin measurements
using Faraday rotation has been successfully implemented in ensembles of
semiconductor spins, read-out of a single semiconductor spin has only been
achieved using transport measurements based on spin-charge conversion. Here, we
demonstrate an all-optical dispersive measurement of the spin-state of a single
electron trapped in a semiconductor quantum dot. We obtain information on the
spin state through conditional Faraday rotation of a spectrally detuned optical
field, induced by the polarization- and spin-selective trion (charged quantum
dot) transitions. To assess the sensitivity of the technique, we use an
independent resonant laser for spin-state preparation. An all-optical
dispersive measurement on single spins has the important advantage of
channeling the measurement back-action onto a conjugate observable, thereby
allowing for repetitive or continuous quantum nondemolition (QND) read-out of
the spin-state. We infer from our results that there are of order unity
back-action induced spin-flip Raman scattering events within our measurement
timescale. Therefore, straightforward improvements such as the use of a
solid-immersion lens and higher efficiency detectors would allow for
back-action evading spin measurements, without the need for a cavity.
