Deterministic Bell state measurement with a single quantum memory

Any quantum information system operates with entanglement as a resource, which should be deterministically generated by a joint measurement known as complete Bell state measurement (BSM). The determinism arises from a quantum nondemolition measurement of two coupled qubits with the help of readout ancilla, which inevitably requires extra physical qubits. We here demonstrate a deterministic and complete BSM with only a nitrogen atom in a nitrogen-vacancy (NV) center in diamond as a quantum memory without reliance on any carbon isotopes by exploiting electron nitrogen (14N) double qutrits at a zero magnetic field. The degenerate logical qubits within the subspace of qutrits on the electron and nitrogen spins are holonomically controlled by arbitrarily polarized microwave and radiofrequency pulses via zero field split states as the ancilla, enabling the complete BSM deterministically. Since the system works under an isotope free and field free environment, the demonstration paves the way for realizing high yield, high fidelity, and high speed quantum repeaters for long haul quantum networks and quantum interfaces for large scale distributed quantum computers.