The implementation of a quantum internet requires the distribution of entanglement over long distances, which is facilitated by entanglement swapping using photonic Bell state measurements (BSMs). Yet, two-photon Bell state measurement schemes have in general a success probability of at best 50%. Here, we propose to overcome this limitation by logically encoding photonic qubits onto photonic tree graph states, an error-correcting code that can be deterministically generated with few matter qubits. We show that we can perform a near-deterministic logical BSM even in the presence of photon losses through two measurement schemes that either use static linear optics or require feed-forward. In addition, we show that these two schemes are also resistant to errors.
The implementation of a quantum internet requires the distribution of entanglement over long distances, which is facilitated by entanglement swapping using photonic Bell state measurements (BSMs). Yet, two-photon Bell state measurement schemes have in general a success probability of at best 50%. Here, we propose to overcome this limitation by logically encoding photonic qubits onto photonic tree graph states, an error-correcting code that can be deterministically generated with few matter qubits. We show that we can perform a near-deterministic logical BSM even in the presence of photon losses through two measurement schemes that either use static linear optics or require feed-forward. In addition, we show that these two schemes are also resistant to errors.