The Quantification of Quantum Nonlocality by Characteristic Function

Quantum nonlocal correlation (QNC) is thought to be more general than quantum entanglement correlation, but the strength of it has not been well defined. We propose a way to measure the strength of QNC basing on the characteristic function. The characteristic function of QNC in a composite system is defined as a response function under the local quantum measurement. It is explored that once a characteristic function is given, the state of a composite system, with just a local trace-preserving quantum operation uncertainty, will be determined. We show that the strength of QNC basing on the characteristic function is a half-positive-definite function and does not change under any LU operation. For a two-partite pure state, the strength of QNC is equivalent to the quantum entanglement. Generally, we give a new definition for quantum entanglement using the strength function. Furthermore, we also give a separability-criterion for 2\timesm-dimensional mixed real matrix. This letter proposes an alternate way for QNC further research.