Loss-tolerant and error-corrected Bell measurement on logical qubits encoded with tree graph states.*

Using linear optics, a two-photon Bell state measurement (BSM) only succeeds with a probability of at best 50%. This limits the performances of many quantum repeater (QR) protocols that use BSM for entanglement swapping. QRs also require loss-tolerance to transfer information at a higher rate than direct fiber transmission and error-correction.

By using either ancillary photonic qubits or nonlinear interaction with atoms, one can overcome the 50% limit but these solutions are neither loss- nor fault-tolerant. Here, we achieve both loss-tolerant and error-corrected BSMs by using a logical encoding that uses photonic tree graph state, which can be efficiently produced with a few matter qubits [1], and by introducing two logical BSM schemes, denoted "static" and "dynamic". The static protocol can be implemented using only linear optics while the dynamic protocol requires feedforward but also yields better performances.

These results can be directly applied to an all-photonic QR protocol that is fault-tolerant, a feature that was lacking in the original proposal [2].

[1] D. Buterakos et al., PRX (2017)
[2] K. Azuma, Nat. Comm. (2015)