Five-mode linear optical scheme for Bell state generation

The capability of linear optics to generate entangled states is widely exploited in quantum information processing, however, it is non-trivial to generate qubit states. Here we investigate the linear optical methods for generation of dual-rail-encoded Bell states using computer optimization. We have found a five-mode scheme that produces these states with probability $1/9$ with heralding by one photon detector. This result is an improvement in both compactness and success probability compared to the previously known schemes requiring six-mode transformations and two photon detectors and providing a success probability of $2/27$. We show that the increase in success probability is due to the elevated order of photon interference implemented by our scheme: four photons interfere in our scheme, while three photons interfere in the known scheme.