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

Abstract: Polarization-entangled photons are the key ingredients of various protocols in quantum computation and quantum key distribution. A near-unity degree of polarization entanglement is essential to minimize qubit error rates in key distribution. This study theoretically investigates the polarization entangled photon pairs produced by a quantum-dot radiative cascade located within a micropillar cavity. To incorporate the unavoidable exciton-phonon coupling in a quantum dot-cavity system, we develop a polaron master equation theory and investigate how it affects the degree of entanglement and qubit error rate. We derive analytical expressions of various phonon-induced incoherent rates and demonstrate that one-photon incoherent rates predominate, substantially diminishing the degree of entanglement. It is shown that at elevated temperatures, the role of cavity-mediated effects such as cross-coupling between exciton states, ac-Stark shift, and multiphoton emission gets reduced owing to the phonon-mediated renormalization of the cavity coupling and Rabi frequency. Finally, we consider a BBM92 quantum key distribution protocol and show the evolution of qubit error rate at elevated temperatures of the phonon bath.