  We demonstrate a one to one correspondence between the polarization state of
a light pulse tuned to neutral exciton resonances of single semiconductor
quantum dots and the spin state of the exciton that it photogenerates. This is
accomplished using two variably polarized and independently tuned picosecond
laser pulses. The first "writes" the spin state of the resonantly excited
exciton. The second is tuned to biexcitonic resonances, and its absorption is
used to "read" the exciton spin state. The absorption of the second pulse
depends on its polarization relative to the exciton spin direction. Changes in
the exciton spin result in corresponding changes in the intensity of the
photoluminescence from the biexciton lines which we monitor, obtaining thus a
one to one mapping between any point on the Poincare sphere of the light
polarization to a point on the Bloch sphere of the exciton spin.
