Spins in semiconductor quantum dots (QDs) are promising local quantum memories to generate polarization-encoded photonic cluster states, as proposed in the pioneering Lindner and Rudolph scheme (2009 Phys. Rev. Lett. 103 113602). However, harnessing the polarization degree of freedom of the optical transitions is hindered by resonant excitation schemes that are widely used to obtain high photon indistinguishability. Here we show that acoustic phonon-assisted excitation, a scheme that preserves high indistinguishability, also allows to fully exploit the polarization selective optical transitions to initialise and measure single spin states. We access the coherence of hole spin systems in a low transverse magnetic field and directly monitor the spin Larmor precession both during the radiative emission process of an excited state or in the QD ground state. We report a spin state detection fidelity of granted by the optical selection rules and a ns hole spin coherence time, demonstrating the potential of this scheme and system to generate linear cluster states with a dozen of photons.
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