Testing Quantum Entanglement with Local Measurement

We propose to detect quantum entanglement by a condition of local measurements. We find that this condition can efficiently detect the pure entangled states for both discrete and continuous variable systems. It does not depend on interference of decoherence from noise and detection loss in some systems, which allows a loophole-free test in real experiments. In particular, it is a necessary condition for the violation of some generalized Bell inequalities.