Macroscopically Nonlocal Quantum Correlations

It is usually believed that coarse-graining of quantum correlations leads to classical in the macroscopic limit. Such a principle, known as locality, has been proved for arising from independent and identically distributed (IID) entangled pairs. In this letter we consider generic (non-IID) scenario. We find Hilbert space structure theory can be preserved This directly Bell violation coarse-grained collective measurements, thus breaking principle locality.