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Ideal projective quantum measurement makes the system state collapse in oneof the observable operator eigenstates $|\phi_\alpha\rangle$, making it apowerful tool for preparing the system in the desired pure state. Nevertheless,experimental realisations of projective measurement are not ideal. During themeasurement time needed to overcome the classical noise of the apparatus, thesystem state is often (slightly) perturbed, which compromises the fidelity ofinitialisation. In this paper, we propose an analytical model to analyse theinitialisation fidelity of the system performed by the single-shot readout. Wederive a method to optimise parameters for the three most used cases of photoncounting based readouts for NV colour centre in diamond, charge state, nuclearspin and low temperature electron spin readout. Our work is of relevance forthe accurate description of initialisation fidelity of the quantum bit when thesingle-shot readout is used for initialisation via post-selection or real-timecontrol.

On readout and initialisation fidelity by finite demolition single shot readout