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A simple protocol for complete and deterministic Bell state measurement isproposed. It consists of measurements of nonlocal spin product operators withthe help of shared entanglement as an ancillary resource. The protocol realizesnot only nonlocal Bell state measurement between a pair of distant qubits butalso a complete Bell filter that transmits either one of the Bell statesindicated by the measurement outcome. These schemes will be useful in quantumtechnologies where nonlocal Bell state measurement is indispensable.

Complete and Deterministic Bell State Measurement Using Nonlocal Spin Products