Estimating entanglement between quantum emitters using directional emission

Recently, it was shown that quantum interference in a system containing a polarized and an unpolarized emitter can allow directional emission of photons into a circulating cavity. Here we ask whether high directionality of photon emission in this system implies a high degree of quantum correlation between the two emitters. We show that the answer is a qualified “yes,” with photon emission directionality and emitter-emitter entanglement showing a monotonic relationship over a broad parameter range. The relationship breaks down only in the limit of perfect directionality. Furthermore, under reasonable assumptions for experimental parameters and stability, we show that the statistics of measured directionality allow a reliable estimate of the concurrence. This result implies that directionality of photon emission in the state preparation stage can be used to determine the entanglement between the emitters, with potential applications to more generic cases including quantum networks.