Experimental proposal for performing nonlocal measurement of a product observable.

Due to the restrictions on quantum measurement imposed by relativistic causality, it is not easy to perform a nonlocal measurement on spacelike separated systems instantaneously. Here we design an experiment in an optical system to perform the nonlocal measurement of a product observable on a two-qubit system, where a maximally-entangled two-qubit state, acting as an ancillary meter, and three identical Kerr media are used to couple the system under consideration and the target meter. It is shown that the nonlocal measurement of the product observable, σzA⊗σzB, which has two degenerate eigenvalues, could be implemented in a deterministic way without violating relativistic causality.