  Giant shell CdSe/CdS quantum dots are bright and flexible emitters, with
near-unity quantum yield and suppressed blinking, but their single photon
purity is reduced by efficient multiexcitonic emission. We report the
observation, at the single dot level, of a large blueshift of the
photoluminescence biexciton spectrum ($24\pm5$ nm over a sample of 32 dots) for
pure-phase wurtzite quantum dots. By spectral filtering, we demonstrate a 2.3
times reduction of the biexciton quantum yield relative to the exciton
emission, while preserving as much as 60% of the exciton single photon
emission, thus improving the purity from $g_2(0)=0.07\pm0.01$ to
$g_2(0)=0.03\pm0.01$. At larger pump fluency the spectral purification is even
more effective with up to a 6.6 times reduction in $g_2(0)$, which is due to
the suppression of higher order excitons and shell states experiencing even
larger blueshift. Our results indicate the potential for synthesis engineered
giant shell quantum dots, with further increased biexciton blueshift, for
quantum optical applications requiring both high purity and brightness.
