Multi-photon emissions constitute a fundamental source of noise in quantum repeaters and other quantum communication protocols when probabilistic photon sources are employed. In this paper, it is shown that by alternating the Bell state measurement (BSM) basis in concatenated entanglement swapping links one can automatically identify and discard many errors from stimulated multi-photon emissions. The proposed protocol is shown to completely eliminate the dominant quadratic growth of multi-photon errors with the length of the repeater chain. Furthermore, it is shown that the protocol can be employed in satellite-assisted entanglement distribution links to enable links which are more robust in the presence of imbalanced channel losses. The analysis introduces a convenient calculus based on Clifford algebra for modeling concatenated entanglement swapping links with multi-photon emissions. In particular, we present a compact expression for the fidelity of the Bell state produced by a repeater chain of arbitrary length including noise from double-pair emissions.
