Quantum repeaters and computation by a single module: Remote nondestructive parity measurement

We introduce a simple photonic probing scheme of remote nondestructive parity measurement (RNPM) on a pair of matter qubits. The protocol works as a single module for key operations such as entanglement generation, Bell measurement, and parity check measurement, which are sufficient not only for building up a quantum repeater but also for equipping it with entanglement distillation. Moreover, the RNPM protocol can also be used for generating cluster states toward measurement-based quantum computation.