Macroscopically Nonlocal Quantum Correlations

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

Figure 1

Macroscopic Bell-type experiment. A source produces a $2N$-particle state and sends half of the particles to Alice and half to Bob. The parties perform collective measurements on their beams, specified by the settings $(p,q)$. For each outcome, local detectors count the number of particles with resolution of the order of $N^{\alpha }$.