Nearly deterministic Bell measurement with multiphoton entanglement for efficient quantum information processing

We present a detailed analysis of the Bell measurement scheme proposed in [Phys. Rev. Lett. 114, 113603 (2015)] based on a logical qubit using Greenberger-Horne-Zeilinger (GHZ) entanglement of photons. The success probability of the proposed Bell measurement can be made arbitrarily high using only linear optics as the number of photons in a logical qubit increases. We compare our scheme with all the other proposals, using single-photon qubits, coherent-state qubits or hybrid qubits, suggested to enhance the efficiency of the Bell measurement. As a remarkable advantage, our scheme requires only photon on-off measurements, while photon number resolving detectors are necessary for all the other proposals. We find that the scheme based on coherent-state qubits shows the best performance with respect to the attained success probability in terms of the average number of photons used in the process, while our scheme outperforms the schemes using single-photon qubits. We finally show that efficient quantum communication and fault-tolerant quantum computation can be realized using our approach.