Macroscopically nonlocal quantum correlations

Abstract

It is usually believed that coarse-graining of quantum correlations leads to classical correlations in the macroscopic limit. Such a principle is known as macroscopic locality. In this letter we re-examine this principle and consider a macroscopic Bell experiment in which parties measure collective observables with a resolution of the order of N α , where N is the number of particles and α defines the level of coarse-graining. One expects nonlocal correlations to fade away as α increases, so the natural question to ask is: what is the value of α required to restore locality, marking the quantum-to-classical transition? In a previous work [M. Navascués and H. Wunderlich, Proc. R. Soc. A. 466: 881 ( 2010)] it was demonstrated that locality is restored at α = 1/2 in the case of independent and identically distributed (IID) entangled pairs. Here we show that this is no longer the case in the generic (non-IID) scenario, where the Hilbert space structure of quantum theory, along with the superposition principle and the Born rule, can survive in the macroscopic limit. This leads straightforwardly to a Bell violation for macroscopic observables, and thus the question of the quantum-to-classical transition remains open.