Accuracy of the Quantum Regression Theorem for Photon Emission from a Quantum Dot

The quantum regression theorem (QRT) is the most widely used tool for calculating multitime correlation functions for the assessment of quantum emitters. It is an approximate method based on a Markov assumption for environmental coupling. In this Letter we quantify properties of photons emitted from a single quantum dot coupled to phonons. For the single-photon purity and the indistinguishability, we compare numerically exact path-integral results with those obtained from the QRT. It is demonstrated that the QRT systematically overestimates the influence of the environment for typical quantum dots used in quantum information technology.