On readout and initialisation fidelity by finite demolition single shot readout

TL;DR

This paper develops an analytical model to analyze and optimize the initialisation fidelity of quantum systems using finite demolition single-shot readout, addressing real-world measurement imperfections.

Contribution

It introduces a new analytical framework and optimization method for photon counting readouts in NV centers, improving initialisation fidelity understanding.

Findings

Derived an analytical model for initialisation fidelity.

Optimized parameters for NV center readouts.

Applicable to post-selection and real-time control.

Abstract

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