Time-bin entanglement in the deterministic generation of linear photonic cluster states

We investigate strategies for the efficient deterministic creation of trains of time-bin entangled photons using an individual quantum emitter described by a $\Lambda$-type electronic system. We explicitly demonstrate generation of high-quality linear cluster states of substantial length in our full microscopic numerical simulations. The underlying scheme is based on the manipulation of ground state coherences through precise optical driving. One important finding is that the most easily accessible quality metrics, the achievable rotation fidelities, fall short in assessing the actual quantum correlations of the emitted photons in the face of losses. To address this, we explicitly calculate stabilizer generator expectation values as a superior gauge for the quantum properties of the many-photon state. Our results illustrate that with controlled minimization of losses and realistic system parameters for quantum-dot type systems, useful linear cluster states of significant lengths can be generated, showcasing promise of scalability for quantum information processing endeavors.