Polarization entanglement and qubit error rate dependence on the exciton-phonon coupling in self-assembled quantum dots

Polarization-entangled photons are key resources for a wide range of protocols in quantum computation and quantum key distribution. Achieving a near-unity degree of polarization entanglement is essential for minimizing qubit error rates in secure key distribution. In this work, we theoretically investigate polarization-entangled photon pairs generated via a quantum-dot radiative cascade embedded in a micropillar cavity. To account for the unavoidable exciton-phonon interactions in the quantum dot-cavity system, we develop a polaron master-equation framework and examine its impact on the degree of entanglement and the resulting qubit error rate. We derive analytical expressions for phonon-induced incoherent scattering rates and show that one-photon incoherent processes dominate, leading to a substantial reduction of entanglement. We further demonstrate that at elevated phonon-bath temperatures, cavity-mediated effects, such as cross-coupling between exciton states, ac Stark shifts, and multiphoton emission, are significantly suppressed due to phonon-induced renormalization of the cavity coupling strength and the Rabi frequency. Finally, we analyze a BBM92 quantum key distribution protocol and study the evolution of the qubit error rate as a function of the phonon-bath temperature.